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1. Completeness And Categoricity: Frege, Godel And Model Theory - History And Philo Frege s project has been characterized as an attempt to formulate a complete system of logic adequate to characterize mathematical theories such http://www.informaworld.com/smpp/621611201-69746491/content~content=a776180580~d

Skip over navigation HOME ABOUT US CONTACT US ... LIBRARIANS Search in entire site Publication Names ISSN/ISBNs Subject Names Author Names Title/Kwds/Abstract or Explore informaworld Journals eBooks Reference Works Allied Health Anthropology Area Studies Arts Behavioral Sciences Bioscience Built Environment Chemistry Communication Studies Computer Science Cultural Studies Dentistry Development Studies Earth Sciences Education Arena Ergonomics Food Science Geography History Law Literature, Language and Linguistics Medicine Pharmaceutical Science Philosophy Physics Religion Social Work Toxicology Urban Studies Browse Publications A-Z Browse ... Got a Voucher? Username: Password: athens sso forgotten password? hide Session timed out - new session started. You may need to sign in again. [ hide message informaworld HOME SEARCH BROWSE Issues List ... Related articles first prev toc next last Download Citation Recommend Mark Alert Link Print hide Please choose the type of alert you would like: Citation Alert New citations of this Article will trigger an alert New Issue Alert New issues of History and Philosophy of Logic will trigger an alert iFirst Alert New iFirst articles in History and Philosophy of Logic will trigger an alert Note: To be alerted to new content in all related publications, please click on one of the subject areas below and select

2. 03Cxx 03C35 Categoricity and completeness of theories; 03C40 Interpolation, preservation, 03C62 Models of arithmetic and set theory See also 03Hxx http://www.ams.org/msc/03Cxx.html

Home MathSciNet Journals Books ... Contact Us 201 Charles Street Providence, RI 02904 USA Phone: 401-455-4000 or 800-321-4AMS Or email us at ams@ams.org Open Positions Model theory 03C05 Equational classes, universal algebra [See also 03C07 Basic properties of first-order languages and structures 03C10 Quantifier elimination, model completeness and related topics 03C13 Finite structures [See also 03C15 Denumerable structures 03C20 Ultraproducts and related constructions 03C25 Model-theoretic forcing 03C30 Other model constructions 03C35 Categoricity and completeness of theories 03C40 Interpolation, preservation, definability 03C45 Classification theory, stability and related concepts 03C50 Models with special properties (saturated, rigid, etc.) 03C52 Properties of classes of models 03C55 Set-theoretic model theory 03C57 Effective and recursion-theoretic model theory [See also 03C60 Model-theoretic algebra [See also 03C62 Models of arithmetic and set theory [See also 03C64 Model theory of ordered structures; o-minimality 03C65 Models of other mathematical theories 03C68 Other classical first-order model theory 03C70 Logic on admissible sets 03C75 Other infinitary logic 03C80 Logic with extra quantifiers and operators [See also 03C85 Second- and higher-order model theory 03C90 Nonclassical models (Boolean-valued, sheaf, etc.)

3. 03Cxx 03C35, Categoricity and completeness of theories. 03C40, Interpolation, preservation, definability. 03C45, Classification theory, stability and related http://www.impan.gov.pl/MSC2000/03Cxx.html

Model theory Equational classes, universal algebra [See also Basic properties of first-order languages and structures Quantifier elimination, model completeness and related topics Finite structures [See also Denumerable structures Ultraproducts and related constructions Model-theoretic forcing Other model constructions Categoricity and completeness of theories Interpolation, preservation, definability Classification theory, stability and related concepts Models with special properties (saturated, rigid, etc.) Properties of classes of models Set-theoretic model theory Effective and recursion-theoretic model theory [See also Model-theoretic algebra [See also Models of arithmetic and set theory [See also Model theory of ordered structures; o-minimality Models of other mathematical theories Other classical first-order model theory Logic on admissible sets Other infinitary logic Logic with extra quantifiers and operators [See also Second- and higher-order model theory Nonclassical models (Boolean-valued, sheaf, etc.) Abstract model theory Applications of model theory [See also None of the above, but in this section

4. HeiDOK 03C35 Categoricity and completeness of theories ( 0 Dok. ) 03C40 Interpolation, preservation, definability ( 0 Dok. ) 03C45 Classification theory http://archiv.ub.uni-heidelberg.de/volltextserver/msc_ebene3.php?zahl=03C&anzahl

5. List KWIC DDC22 510 And MSC+ZDM E-N Lexical Connection theories Categoricity and completeness of 03C35 theories categories and 18Cxx theories classical field 70Sxx theories existence 49Jxx http://www.math.unipd.it/~biblio/kwic/msc-cdd/dml2_11_58.htm

textbooks, tutorial papers, etc.) # instructional exposition ( textbooks, tutorial papers, etc.) # instructional exposition ( textbooks, tutorial papers, etc.) # instructional exposition ( textbooks. textbook use in the classroom # analysis of textbooks, development and evaluation of texture th and 16th centuries, renaissance # 15 th centuries, renaissance # 15th and 16 th century # 17 th century # 18 th century # 19 th century # 20 th problem and ramifications) # theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16 theorem # Hilbertian fields; Hilbert's irreducibility theorem proving (deduction, resolution, etc.) theorem, asphericity # Dehn's lemma, sphere theorem, loop theorem, loop theorem, asphericity # Dehn's lemma, sphere theorem. polynomials. finite sums) # elementary algebra (variables, manipulation of expressions. binomial theorems # $L^p$-limit theorems # abstract inverse mapping and implicit function theorems # algebraic dependence theorems # analytic algebras and generalizations, preparation

6. John Corcoran Homepage Future Research on Ancient theories of Communication and Reasoning, ibid. . A note on Categoricity and completeness, History and Philosophy of Logic 2 http://www.acsu.buffalo.edu/~corcoran/pubs.htm

Welcome to the homepage of John Corcoran Contact Information Curriculum Vitae Courses Contact me ... via email Complete List of Publications: (Last updated October 2004) I. Articles II. Abstracts III. Books (editor) IV. Miscellaneous ... Printable list of publications (PDF), or see Taylor and Francis Online Journals (sign-in required). PDF requires free Acrobat Reader software. I. Articles: MR indicates review in Mathematical Reviews available at MathSciNet (login required) J indicates available at JSTOR (with online link, login required). G indicates available at Google by entering John Corcoran plus the complete title (with online link). J Three Logical Theories, Philosophy of Science Logical Consequence in Modal Logic: Natural Deduction in S5 (co-author G. Weaver), Notre Dame Journal of Formal Logic Discourse Grammars and the Structure of Mathematical Reasoning I: Mathematical Reasoning and the Stratification of Language

7. List KWIC DDC And MSC Lexical Connection Categoricity and completeness of theories 03C35 categories Abelian 18Exx categories accessible and locally presentable 18C35 http://www.mi.imati.cnr.it/~alberto/dml_11_05.htm

Boolean functions Boolean programming Boolean rings) # Boolean algebras ( Boolean rings, measure algebras # measures on Boolean-valued models # other aspects of forcing and Boolean-valued, sheaf, etc.) # nonclassical models ( bootstrap, jackknife and other resampling methods bordism and cobordism theories, formal group laws Borel, analytic, projective, etc. sets) # descriptive set theory (topological aspects of bornologies and related structures; Mackey convergence, etc. botanic sciences boundaries # dynamics of phase boundaries # geometric and analytic invariants on weakly pseudoconvex boundaries of domains # CR$ manifolds as boundary # method of contraction of the boundary behavior boundary behavior (theorems of Fatou type, etc.) boundary behavior of holomorphic functions boundary behavior of holomorphic functions # global boundary behavior of power series, over-convergence boundary data, parameters # dependence of solutions of PDE on initial and boundary element methods boundary element methods boundary element methods boundary element methods boundary element methods boundary layers # turbulent boundary problems for PDE # free boundary regularity of mappings boundary theory boundary theory # ideal boundary theory # Martin boundary uniqueness of mappings boundary value and inverse problems boundary value and inverse problems boundary value problems boundary value problems boundary value problems boundary value problems boundary value problems # linear boundary value problems # multipoint

8. Sachgebiete Der AMS-Klassifikation: 00-09 deductive systems 03B25 Decidability of theories and sets of sentences, 03C35 Categoricity and completeness of theories 03C40 Interpolation, http://www.math.fu-berlin.de/litrech/Class/ams-00-09.html

Sachgebiete der AMS-Klassifikation: 00-09 nach 90-99 Weiter nach 10-19 Suche in allen Klassifikationen 01-XX 03-XX 04-XX 05-XX 06-XX 08-XX nach 90-99 Weiter nach 10-19 Suche in allen Klassifikationen

9. Department Of Mathematics, University Of Illinois At Urbana-Champaign Systems of formal proofs and the completeness theorem. Basic elements of model theory (completeness of theories, Categoricity, quantifier elimination) and http://www.math.uiuc.edu/ResearchAreas/logic/exams.html

Logic: Exams Logic Comprehensive Exam Logic Preliminary Exam Thesis and Final Examination Logic Comprehensive Exam Before you decide to take the comprehensive exam in Mathematical Logic check out the overall structure of the comprehensive exam system. Syllabus The Comprehensive Exam in Mathematical Logic may contain problems in the following topics: Syntax and semantics of propositional logic and first order logic. Compactness theorem. Systems of formal proofs and the completeness theorem. Basic elements of model theory (completeness of theories, categoricity, quantifier elimination) and examples such as dense linear orderings, vector spaces, algebraically closed fields, and simple fragments of arithmetic. Incompleteness theorem and related topics, including: basic properties of computable functions, relations and functions representable in a theory, undecidability of various systems of arithmetic, undecidability of pure first order logic, and decidability of certain other theories. S uggestions from a student who passed Make sure you know the topics above.

10. The Development Of Mathematical Logic From Russell To Tarski: 1900-1935 | Richar 1.2 Peano s school on the logical structure of theories, 4. 1.3 Hilbert on axiomatization, 8. 1.4 completeness and Categoricity in the work of Veblen and http://www.ucalgary.ca/~rzach/papers/history.html

@import "/rzach/misc/drupal.css"; @import "http://www.ucalgary.ca/templates2/styles/uofc-level-c.css"; @import "/rzach/files/rzach/custom_colors/uofc_c_v7.css"; Skip to Headline Skip to Navigation Skip to Content Skip to Sidebar UofC Navigation Prospective Students Current Students Alumni Community Search UofC: IT MY U OF C Contacts Richard Zach Site Navigation Primary links Home Research Teaching CV ... LogBlog Research and Publications History of Logic Kurt G¶del and computability theory Hilbert's "Verungl¼ckter Beweis," the first epsilon theorem, and consistency proofs The Development of Mathematical Logic from Russell to Tarski: 1900-1935 ... Other Logic Search Navigation search The Development of Mathematical Logic from Russell to Tarski: 1900-1935 Source Leila Haaparanta, ed., The History of Modern Logic . New York and Oxford: Oxford University Press, to appear. 178 pp. (with Paolo Mancosu and Calixto Badesa) Abstract The period from 1900 to 1935 was particularly fruitful and important for the development of logic and logical metatheory. This survey is organized along eight "itineraries" concentrating on historically and conceptually linked strands in this development. Itinerary I deals with the evolution of conceptions of axiomatics. Itinerary II centers on the logical work of Bertrand Russell. Itinerary III presents the development of set theory from Zermelo onward. Itinerary IV discusses the contributions of the algebra of logic tradition, in particular, L¶wenheim and Skolem. Itinerary V surveys the work in logic connected to the Hilbert school, and itinerary V deals specifically with consistency proofs and metamathematics, including the incompleteness theorems. Itinerary VII traces the development of intuitionistic and many-valued logics. Itinerary VIII surveys the development of semantical notions from the early work on axiomatics up to Tarski's work on truth.

11. Springer Online Reference Works Based on predicate calculus various logicomathematical theories have been and questions of Categoricity and completeness of classes of models. http://eom.springer.de/m/m062660.htm

Encyclopaedia of Mathematics M Article referred from Article refers to Mathematical logic, symbolic logic The branch of mathematics concerned with the study of mathematical proofs and questions in the foundation of mathematics. Historical sketch. The idea of constructing a universal language for the whole of mathematics, and of the formalization of proofs on the basis of such a language, was suggested in the 17th century by G. Leibniz . But not until the middle of the 19th century did there appear the first scientific work on the algebraization of Aristotelean logic ( G. Boole , A. de Morgan ). After G. Frege ) and C. Peirce ) put the logic of predicates, variables and quantifiers into the language of algebra, it became possible to apply this language to questions in the foundations of mathematics. On the other hand, the creation of non-Euclidean geometry in the 19th century K. Weierstrass R. Dedekind and G. Cantor , and G. Peano ). In this connection, Peano created a more suitable symbolic representation for the language of logic. Afterwards, this language was perfected in the joint work of B. Russell

12. UC Berkeley - Department Of Philosophy “From the DeductiveNomological Model to Unification theories of Explanation” Mexico City, “On completeness and Categoricity of Deductive Systems” http://philosophy.berkeley.edu/people/page/7

Paolo Mancosu Talks Invited talks since 2004 1/17/2004, Feferman Symposium, Stanford University, “Tarski on models and logical consequence”, 1/30/2004, Mathematics in the Humanities Series, Stanford University, “The varieties of mathematical explanation”, 3/5/2004, Workshop on Methodology of Pure and Applied Mathematics, Laguna Beach, “Visualization in Logic and Mathematics”. 4/23/ 2004, Logic Colloquium, UCLA, Los Angeles, “Tarski on models and logical consequence”, 5/21/2004, Congr¨s d’histoire des sciences et des techniques, Poitiers, “Tendences actuelles en histoire et philosophie des math©matiques aux USA”. 5/27/2004, College de France, Paris, “Logic, mathematics and the finiteness of the world: the discussion between Tarski and Carnap in 1941”. 6/16/2004, Maison Suger, Paris, Colloque “Fondements et justification des pratiques en math©matiques, “The varieties of mathematical explanation” 8/27/2004, University of Uppsala, Sweden, International Workshop “Logicism, Intuitionism, Formalism: What has become of them?”, “Predicativity: Problems and Prospects,” 9/2/2004, Mathematics Department, Uppsala University, “Tarski on models and logical consequence”

13. Faculty Of Science -Department Of MACS-Course Synopses FirstOrder axiomatics theories. Consistency and satisfiability of Sets formula. Consistency, completeness and Categoricity of First-Order theories. http://www.nul.ls/faculties/science/macs_gsynopses.htm

V isitors Contacts Sitemap Feedback ... Students Affairs Department of MACS - Graduate Course Synopses PM 561 - Abstract Algebra: ( 6 c.h) 1. Ordered sets: Example from mathematics, computer science and social science. Diagrams, Maps between ordered sets. The Duality principle. Maximal and minimal elements; top and bottom. Building new ordered sets. 2. Lattices and complete lattices: Lattices as ordered sets. Complete lattices chain condition and completeness. Completions (Dedekind-MacNeille completion). 3. CPOS. Algebraic lattices and domains: Directed joins and algebraic closure operators. CPOS (complete partial ordered sets) Finiteness, algebraic lattices and domains. Information systems. 4. Ideals and filters: Ideals and filters. Prime ideals, maximal ideal and ultrafilters. The existence of prime ideals, maximal ideals and ultrafilters. 5. Representation theory: Representation by lattices of sets. The prime ideal space (Stone’s representation theorem for Boolean algebra). Priestley’s representation theorem for distributive lattice.

14. PlanetMath: Vaught's Test Keywords, model theory, logic AMS MSC, 03C35 (Mathematical logic and foundations Model theory Categoricity and completeness of theories) http://planetmath.org/encyclopedia/VaughtsTest.html

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... RSS Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About Vaught's test (Theorem) Let be a first order language , and let be a set of -sentences with no finite models which is -categorical for some . Then is complete "Vaught's test" is owned by Evandar view preamble View style: HTML with images page images TeX source See Also: -categorical Keywords: model theory, logic Attachments: proof of Vaught's test (Proof) by Evandar Log in to rate this entry. view current ratings Cross-references: finite first order language This is version 4 of Vaught's test , born on 2002-08-29, modified 2002-09-04. Object id is , canonical name is VaughtsTest Accessed 1660 times total. Classification: AMS MSC (Mathematical logic and foundations :: Model theory :: Categoricity and completeness of theories) Pending Errata and Addenda None.

15. STATE UNIVERSITY COLLEGE AT BUFFALO Isomorphism and Categoricity. c. Decidability. 6. theories with equality MAT 431 MATHEMATICAL LOGIC Validity, deducibility, and completeness in http://math.buffalostate.edu/~math/courses/undergraduate/mat 431.html

STATE UNIVERSITY COLLEGE AT BUFFALO Department of Mathematics Request for Course I. Number and title of course MAT 431 - Mathematical Logic II. Reasons for addition to the present curricula A. The course, an extension of MAT 270. will consist of topics in mathematical logic not covered in courses presently offered. B. The course should enable the student to better appreciate the axiomatic method in mathematics. C. The course provides a study of formal systems in contrast to informal systems which is the usual way topics in all other mathematics courses are presented. D. The course should help prepare the student for more formally structured graduate mathematics courses. E. While other courses may emphasize skills and knowledge in special areas of mathematics, this course allows the student to understand the abstract nature and structure of all of mathematics. III. Major objectives of the course A. To acquaint the student with a basic knowledge of mathematical logic. B. To help the student better understand the precise roles of set theory and quantification logic in mathematics in providing a uniform language and basis for all of mathematics. C.

16. General General Mathematics Mathematics For Nonmathematicians model completeness and related topics Finite structures See also 68Q15, constructions Categoricity and completeness of theories Interpolation, http://amf.openlib.org/2001/msc2000.xsd

17. UoY - CS - AIG completeness and Categoricity in RegionBased theories of Space This means that the entailments provable in the RCC theory are only those that hold in a http://www.cs.york.ac.uk/aig/seminars/96.php

AI Group: Seminars held in 2005 March 11th Formal reasoning in the Z notation using the CADiZ toolset Ian Toyn University of York Abstract The Z notation is used for formal specifications of systems. CADiZ is a set of tools for manipulating Z specifications. It extends an existing document preparation system (troff/latex/word) with a type-checker for the mathematical paragraphs of a specification and a browser based on a document previewing tool. Having established this effective browsing interface, some reasoning abilities have been added that are accessed through the same user interface. The result is a theorem prover whose user interface is superior, but whose reasoning abilities are as yet inferior, compared to most good theorem provers. This seminar will take the form of an on-line demonstration of CADiZ using a portable computer linked to a video projector. April 11th A Topological Transition Based Logic for the Qualitative Motion of Objec ts Andre Trudel Jodrey School of Computer Science, Acadia University, Nova Scotia, Canada Abstract We present a spatio-temporal ontology suitable for representing and reasoning about the qualitative motion of rigid bodies. This simple ontology provides a uniform treatment of motion in one, two, and three dimensional space. A succinct axiomatization is provided capturing the ontology. This first order logic is based on the transition of topological relations between objects.

18. Steve Awodey S. Awodey and H. Forssell, Theory and Applications of Categories 15(5), CT 2004, Categoricity and completeness 19th century axiomatics to 21st century http://www.andrew.cmu.edu/~awodey/

Steve Awodey Associate Professor Department of Philosophy Carnegie Mellon University Research Areas Category Theory Logic Philosophy of Mathematics History of Logic and Analytic Philosophy Research Connections: Algebraic Set Theory Logic of Types and Computation New book, now available! Category Theory , Oxford Logic Guides, Oxford University Press, 2006 Click here for more information. Selected Current Preprints An outline of algebraic set theory. S. Awodey, January 2006. Algebraic models of theories of sets and classes. S. Awodey, H. Forssell, M. Warren, June 2006. Relating topos theory and set theory via categories of classes. S. Awodey, C. Butz, A. Simpson, T. Streicher, June 2003. Sheaf toposes for realizability. S. Awodey and A. Bauer, (2002), forthcoming in: Archive for Mathemtical Logic Continuity and logical completeness [ps] [pdf]. S. Awodey, December 2000. Selected Publications Algebraic models of intuitionistic theories of sets and classes. S. Awodey and H. Forssell, Theory and Applications of Categories 15(5), CT 2004, pp. 147163 (2004).

19. JSTOR 2000-2001 Spring Meeting Of The Association For Symbolic Logic Speakers and topics in the Reverse Mathematics and Computability Theory . 2 S. AWODEY and E.H. RECK, completeness and Categoricity 19th century http://links.jstor.org/sici?sici=1079-8986(200109)7:3<413:2SMOTA>2.0.CO;2-W

20. Model Theory - Wikipedia, The Free Encyclopedia edit Elimination of quantifiers and model completeness . edit Categoricity. If T is a first order theory in the language L and is a cardinal, http://en.wikipedia.org/wiki/Model_theory

var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia"; Model theory From Wikipedia, the free encyclopedia Jump to: navigation search This article discusses model theory as a mathematical discipline and not the term mathematical model which is used informally in other parts of mathematics and science. In mathematics model theory is the study of (classes of) mathematical structures such as groups fields graphs or even models of set theory using tools from mathematical logic . Model theory has close ties to algebra and universal algebra This article focuses on finitary first order model theory of infinite structures. The model theoretic study of finite structures (for which see finite model theory ) diverges significantly from the study of infinite structures both in terms of the problems studied and the techniques used. Model theory in higher-order logics or infinitary logics is hampered by the fact that completeness does not in general hold for these logics. However, a great deal of study has also been done in such languages. Contents The role of model theory The areas of model theory Universal algebra Finite model theory ... Axiomatizability, elimination of quantifiers, and model-completeness

21. Equivalence Of Strong Completeness And Categoricity - Sci.logic | Google Groups ~F so T adjoin F is an inconsistent theory. Now, strong completeness implies Categoricity Again, if F is a theorem then you re done. http://groups.google.bs/group/sci.logic/msg/8ebc7f1227d3dc1a

Help Sign in sci.logic Discussions ... Subscribe to this group This is a Usenet group - learn more Message from discussion Equivalence of Strong completeness and categoricity The group you are posting to is a Usenet group . Messages posted to this group will make your email address visible to anyone on the Internet. Your reply message has not been sent. Your post was successful William Boshuck View profile More options Jul 27 1992, 12:25 pm Newsgroups: sci.logic From: bosh @triples.math.mcgill.ca (William Boshuck) Date: Tue, 28 Jul 92 02:52:11 GMT Local: Mon, Jul 27 1992 10:52 pm Subject: Re: Equivalence of Strong completeness and categoricity Reply to author Forward Print View thread ... Find messages by this author @cenatls.cena.dgac.fr (Jean-Marc Alliot) writes: The proof which answers question 1) depends on something called the deduction theorem which, in turn gives an answer to the second question. The deduction theorem says that for a theory T and formulas F,G, that the following inferences (both top to bottom and bottom to top) are valid under consideration) In some treatments of logic, this is

22. FOM: The Blind Spot About Theory-completeness And Categoricity I have been researching the origins of logicians grasp of the concepts of theorycompleteness and Categoricity, and have uncovered what I regard as an http://cs.nyu.edu/pipermail/fom/1997-December/000548.html

FOM: the blind spot about theory-completeness and categoricity Neil Tennant neilt at hums62.cohums.ohio-state.edu Tue Dec 16 11:22:32 EST 1997 Previous message: FOM: Reply to Machover on Conclusiveness addendum Next message: FOM: the blind spot about theory-completeness and categoricity Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... tennant.9 at osu.edu ) I shall send you hard copy when the paper is ready. Those with whom I have already been corresponding and to whom a copy has been promised need not reply! The current, tentative title is 'Mathematics: Intuition and Structure'. As you will be able to tell from the above acknowledgements, I really do not think this paper would have come about without the stimulation and resources provided by fom. So season's greetings, tinged with gratitude, to Steve, for getting it all going! Previous message: FOM: Reply to Machover on Conclusiveness addendum Next message: FOM: the blind spot about theory-completeness and categoricity Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... More information about the FOM mailing list

23. Model Theory | Mathematical Institute - University Of Oxford The concepts of completeness and Categoricity will be studied and some more advanced technical notions, up to elements of modern stability theory, http://www.maths.ox.ac.uk/courses/mfocs/model-theory

@import "/modules/aggregator/aggregator.css"; @import "/modules/node/node.css"; @import "/modules/system/defaults.css"; @import "/modules/system/system.css"; @import "/modules/user/user.css"; @import "/./sites/all/modules/calendar/calendar.css"; @import "/sites/all/modules/cck/content.css"; @import "/sites/all/modules/drutex/drutex.css"; @import "/sites/all/modules/event/event.css"; @import "/sites/all/modules/calendar/calendar.css"; @import "/sites/all/modules/date/date.css"; @import "/sites/all/modules/cck/fieldgroup.css"; @import "/sites/all/themes/maths/style.css"; Skip navigation Locator: Home » View Model Theory Main Home Prospective Students Current Students Teaching Staff ... About Us Departmental Members Login Username: Password: Model Theory HT View course material Number of lectures: 16 HT Lecturer(s): Boris Zilber Course Description Recommended Prerequisites This course presupposes basic knowledge of First Order Predicate Calculus up to and including the Soundness and Completeness Theorems. Also a familiarity with (at least the statement of) the Compactness Theorem would also be desirable. The course deepens student’s understanding of the notion of a mathematical structure and of the logical formalism that underlies every mathematical theory, taking B1 Logic as a starting point. Various examples emphasise the connection between logical notions and practical mathematics.

24. IngentaConnect Towards Completeness: Husserl On Theories Of Manifolds 18901901 Towards completeness Husserl on theories of manifolds 18901901 shows that Husserl meant by definiteness what is today called `Categoricity . http://www.ingentaconnect.com/content/klu/synt/2007/00000156/00000002/00000008

var tcdacmd="dt"; Home About Ingenta Ingenta Labs Ingenta Blog ... Check our FAQs Or contact us to report problems with: Subscription access Article delivery Registration Library administrator tasks ... Other problems For Publishers Why go online? Why choose IngentaConnect? Beyond Print: enhancing your service Access and authentication ... Contact us For Researchers For Authors About IngentaConnect Search and browse Publications available ... Register For Librarians Resource Zone Why choose IngentaConnect? Why choose IngentaConnect Complete? Activating Subscriptions ... Register CM8ShowAd("HorizontalBanner"); Towards completeness: Husserl on theories of manifolds 1890-1901 Author: Hartimo, Mirja Source: Synthese , Volume 156, Number 2, May 2007 , pp. 281-310(30) Publisher: Springer view table of contents Key: - Free Content - New Content - Subscribed Content - Free Trial Content CM8ShowAd("Skyscraper"); Abstract: Husserl's notion of definiteness, i.e., completeness is crucial to understanding Husserl's view of logic, and consequently several related philosophical views, such as his argument against psychologism, his notion of ideality, and his view of formal ontology. Initially Husserl developed the notion of definiteness to clarify Hermann Hankel's `principle of permanence'. One of the first attempts at formulating definiteness can be found in the Philosophy of Arithmetic Keywords: Early Husserl Definiteness Completeness Theories of manifolds Document Type:

25. Category Theory > Alphabetically Sorted, Complete Bibliography (Stanford Encyclo Awodey, S. Reck, E. R., 2002, completeness and Categoricity I. Baianu, I. C., 1987, Computer Models and Automata Theory in Biology and Medecine , http://plato.stanford.edu/entries/category-theory/bib.html

Cite this entry Search the SEP Advanced Search Tools ... Stanford University Supplement to Category Theory Alphabetically Sorted, Complete Bibliography Adamek, J. et al Abstract and Concrete Categories: The Joy of Cats , New York: Wiley. Adamek, J. et al ., 1994, Locally Presentable and Accessible Categories, Cambridge: Cambridge University Press. Annals of Mathematics and Artificial Intelligence Journal of Symbolic Logic History and Philosophy of Logic History and Philosophy of Logic Awodey, S., 1996, "Structure in Mathematics and Logic: A Categorical Perspective", Philosophia Mathematica Awodey, S., 2004, "An Answer to Hellman's Question: Does Category Theory Provide a Framework for Mathematical Structuralism", Philosophia Mathematica Awodey, S., 2006, Category Theory , Oxford: Clarendon Press. n -Categories and the Algebra of Opetopes", Advances in Mathematics Higher Category Theory , Contemporary Mathematics, Baez, J., 1997, "An Introduction to n -Categories", Category Theory and Computer Science , Lecture Notes in Computer Science, Baianu, I. C., 1987, "Computer Models and Automata Theory in Biology and Medecine", in Witten, Matthew, Eds.

26. Publications In Logic Fundamentals of Stability Theory, SpringerVerlag, 1988, XIII+ 447 pages. Categoricity and generalized model completeness, (withG. Ahlbrandt), Z. Math. http://www.math.uic.edu/~jbaldwin/pmodel.html

Publications in Logic John T. Baldwin On strongly minimal sets, (with A. H. Lachlan), J. SymbolicLogic 36 (1971), 79-96. Alpha T is finite for aleph-one categorical T, Trans.Amer. Math. Soc. 181 (1973), 37-51. Almost strongly minimal theories I, J. Symbolic Logic 37(1972), 481-493. Almost strongly minimal theories II, J. Symbolic Logic 37(1972), 657-660. The number of automorphisms of a model of an aleph-onecategorical theory, Fund. Math., (1) 83 (1973), 1-6. On universal Horn theories categorical in some infinitepower, (with A. H. Lachlan), Algebra Universalis (fasc. 1) 3 (1973),98-111. A sufficient condition for a variety to have the amalgamationproperty, Colloq. Math. (fasc. 2) XXVIII (1973), 81-83. A "natural" theory without a prime model, (with A. Blass,D.W. Kueker and A.M.W. Glass), Algebra Universalis (fasc. 2)3 (1973), 152-155. A topology for the space of countable models of a first ordertheory, (with J. M. Plotkin), Z. Math. Logik Grundlag.Math. 20 (1974) 173-178. Atomic compactness and aleph-one categorical Horntheories, Fund. Math. LXXXII (1975), 7-9. Conservative extensions and the two cardinal theoremfor stable theories, Fund. Math. LXXXVIII (1975), 7-9.

27. Historia Matematica Mailing List Archive: [HM] Categorical Systems concepts and methods in model theory, universal algebra and category theory that cover completeness for Categoricity appeared as a consequence of http://sunsite.utk.edu/math_archives/.http/hypermail/historia/oct99/0042.html

[HM] Categorical systems Carlos Cesar de Araujo carlos.cesar@taskmail.com.br 10 Oct 99 18:58:47 -0400 (EDT) Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Next message: Antreas P. Hatzipolakis: "Re: [HM] An Italian archive" Previous message: Antreas P. Hatzipolakis: "Re: [HM] Pick's Theorem" Next in thread: Luigi Borzacchini: "Re: [HM] Categorical systems" As Zach [1] recently pointed out (p.353), "The history of the concept(s) of completeness of an axiomatic system has yet to be written". Be that as it may, there is no doubt that one starting point here is Hilbert's "axiom of completeness". Note that "completeness" is first used by him to name just an axiom and not a PROPERTY OF an axiom system. "Completeness" in this latter sense (and in many forms) would be very much investigated by Hilbert himself and his collaborators in the 1920s. Zach [1] is right when he remarks (p.353) that "one of the roots of completeness as a property of axiom systems is the completeness axiom that Hilbert introduced in" [2].

28. UCR Faculty Directory: Individual Listing completeness and Categoricity, Part II 20th Century Metalogic to 21st The Development of Metamathematics and Proof Theory (with Jeremy Avigad), http://www.facultydirectory.ucr.edu/cgi-bin/pub/public_individual.pl?faculty=181

29. Completeness » SlideShare ANDREJKO completeness. Slide 10 COMPLETNESS Categoricity COMPLETE theories THEOREM Let be an L theory. Suppose for some L for all M, http://www.slideshare.net/andrejko/completeness/

Uploading Slideshare.net (beta) Home My Slidespace Upload Community ... Slidecasts Post: Download file close addthis_url = location.href; addthis_title = document.title; addthis_pub = 'slideshare'; All Comments Comments on Slide 1 Add a comment All comments Add a comment on Slide 1 If you have a SlideShare account, login to comment; else you can comment as a guest Embed Video? Just include the embed code in the comment! We support embeds from Youtube, Google Videos, BlipTV, Metacafe, DailyMotion, Viddler and several other approved sites only Are you human? (Sorry for asking) Enter the text in the image (Cannot see the image? Reload image Showing 1-50 of ( more Completeness From: andrejko , 4 months ago embed ( Stats Share this slideshow Tags No tags to display Groups Not added to any group Privacy Info New! This slideshow is Public Embed in your blog Embed ( wordpress.com Related Slideshows Decidability from: andrejko views Completeness from: andrejko views Compactness from: andrejko views ZF from: andrejko views Ordinal Cardinals from: andrejko views Basic S and L : The existence of an S-space under MA...

30. Course Number Generalized Functions, Theory of Distribution, Green Functions and Boundary Value . of Models Categoricity in Power, Element Types, Model completeness, http://math.korea.ac.kr/www_old/english version/curriculum/graduate_courses.html

Graduate Courses Course Number Title Course Description IA 501 Algebra I Group, Ring, Field, Vector Space, Structure of Ring, Abelian Group IA 502 Algebra II Real Number Field, Lebesque Measure, Lebesque Measurable Function, Lebesque Integration, Differentiation and Integration, Space of Measurable Functions IA 503 Topology I Topological Space, Identification Topology, Connectiveness, Separation, Metric Space IA 504 Geometry Curve, Surface, Shape Operator, Surface Geometry, Riemann Geometry IA 505 Probability I Relationship between Probability and Real Analysis, Law of Large Number, Conditional Expectation, Martingale, Ergodic Theory IA 506 Applied Mathematics I Generalized Functions, Theory of Distribution, Green Functions and Boundary Value Problems, Fourier Transformation IA 507 Complex Analysis Conformal Mapping, Application of conformal Mapping, Schwarz-Christoffel Transformation, Poisson Integration Formula, Analytic Continuation IA 601 Algebra II Noetherian Ring and Abelian Group, Primary Decomposition, Localization and Tensor Product, Local Ring, Completeness

31. Logic Seminars 1997-98 Effective completeness theorem; model completeness and decidability. September 4, 1997 Computable Categoricity and degree spectra. January 29, 1998 http://www.math.cornell.edu/~shore/sem978.html

Logic Seminars September 2, 1997 Suman Ganguli, Cornell University Effective completeness theorem; model completeness and decidability September 4, 1997 Reed Solomon, Cornell University Computable presentations of structures of low degree September 9, 1997 Robert Milnikel, Cornell University Omitting types and decidability September 11, 1997 Joe Miller, Cornell University Avoidable algebraic sets in Euclidean space September 16, 1997 Robert Milnikel, Cornell University Omitting types and decidability II September 18, 1997 Joe Miller, Cornell University Avoidable algebraic sets in Euclidean space II September 23, 1997 Robert Milnikel, Cornell University Omitting types and decidability September 25, 1997 Denis Hirschfeldt , Cornell University The Baldwin-Lachlan theorem September 30, 1997 Robert Milnikel , Cornell University Omitting types and decidability II October 5, 1997 Denis Hirschfeldt, Cornell University The Baldwin-Lachlan theorem II October 7, 1997 Richard Shore, Cornell University Decidable prime models October 16, 1997

32. Tree Structure Of LoLaLi Concept Hierarchy Updated On 2004624 219 completeness of theories . . . . 235 saturation . 218 Categoricity g . . . . 220 definability . . . . 226 interpolation . http://remote.science.uva.nl/~caterina/LoLaLi/soft/ch-data/tree.txt

Tree structure of LoLaLi Concept Hierarchy Updated on 2004:6:24, 13:16 In each line the following information is shown (in order from left to right, [OPT] indicates information that can be missing): Type of relation with the parent concept (see below for the legend) [OPT] Id of the node Name of the node Number of children, in parenthesis [OPT] + if the concept is repeated somehwere [OPT] (see file path.txt for the list of repeated nodes) LEGEND: SbC Subclass Par Part-of Not Notion Res Mathematical results His historical view Ins Instance Uns Unspecified top (4) g . 87 computer science (4) g . . 191 logic (1) (31) + g . . . Par 53 automated reasoning (25) + . . . . 35 belief revision . . . . . 76 update . . . . 67 nonmonotonic reasoning . . . . 63 mathematical induction . . . . 71 rewrite system (3) . . . . . 350 termination . . . . . 348 confluence . . . . . 349 critical pair . . . . 70 resolution (7) + . . . . . 339 purity principle . . . . . 342 simplification . . . . . 337 demodulation . . . . . 338 ordering . . . . . 340 removal of tautologies . . . . . 341 resolution refinement (4) . . . . . . 345 lock resolution . . . . . . 344 hyper resolution . . . . . . 347 theory resolution . . . . . . 346 set of support . . . . . 343 subsumption . . . . 68 paramodulation . . . . Not 72 skolemisation . . . . 65 model checking . . . . 55 clause 55 (2) . . . . . 80 horn clause g . . . . . 79 Gentzen clause . . . . 74 uncertainty . . . . 75 unification + . . . . 57 connection graph procedure . . . . 64 metatheory . . . . 61 literal . . . . 58 connection matrix . . . . 81 clause 81 . . . . . SbC 82 relative clause . . . . 69 reason extraction . . . . 59 deduction (7) + . . . . . Not 109 inconsistency . . . . . 106 consequence g . . . . . SbC 494 labelled deductive system . . . . . 111 rule-based deduction . . . . . Not 108 entailment + . . . . . 110 natural deduction (2) + g . . . . . . Not 482 hypothetical reasoning + . . . . . . Not 483 normalization . . . . . Not 107 consistency + . . . . Res 60 Herbrand's theorem . . . . 56 completion . . . . . 86 Knuth Bendix completion . . . . 73 theorem prover (3) . . . . . 427 Bliksem g . . . . . 428 Boyer-Moore theorem prover . . . . . 429 SPASS g . . . . 66 narrowing . . . . 62 logic programming g . . . . 54 answer extraction . . . . 247 nonmonotonic logic + g . . . . . 248 default inference . . . Par 198 proof theory (22) g . . . . SbC 503 sequent calculus . . . . . Not 484 structural rules . . . . 289 interpretation . . . . 282 constructive analysis . . . . 295 recursive ordinal . . . . 287 Goedel numbering . . . . 288 higher-order arithmetic . . . . 281 complexity of proofs . . . . 294 recursive analysis . . . . Res 292 normal form theorem . . . . 297 second-order arithmetic . . . . SbC 110 natural deduction (2) + g . . . . . Not 482 hypothetical reasoning + . . . . . Not 483 normalization . . . . 290 intuitionistic mathematics . . . . 286 functionals in proof theory . . . . 298 structure of proofs g . . . . 283 constructive system . . . . 291 metamathematics . . . . 59 deduction (7) + . . . . . Not 109 inconsistency . . . . . 106 consequence g . . . . . SbC 494 labelled deductive system . . . . . 111 rule-based deduction . . . . . Not 108 entailment + . . . . . 110 natural deduction (2) + g . . . . . . Not 482 hypothetical reasoning + . . . . . . Not 483 normalization . . . . . Not 107 consistency + . . . . 296 relative consistency . . . . Not 284 cut elimination theorem g . . . . 293 ordinal notation . . . . 285 first-order arithmetic . . . . SbC 485 proof nets . . . SbC 475 first order logic (4) g . . . . 254 quantifier (5) + g . . . . . Not 516 bound variable + g . . . . . His 514 Frege on quantification + g . . . . . Not 517 free variable + g . . . . . His 513 Aristotle on quantification + . . . . . Not 301 scope . . . . . . 351 scoping algorithm . . . . Par 476 first order language g . . . . . Not 477 fragment (3) g . . . . . . SbC 479 finite-variable fragment g . . . . . . SbC 480 guarded fragment g . . . . . . SbC 478 modal fragment g . . . . . . . Not 470 standard translation + g . . . . 511 SPASS g . . . . Par 515 quantification (4) + . . . . . Not 516 bound variable + g . . . . . His 514 Frege on quantification + g . . . . . Not 517 free variable + g . . . . . His 513 Aristotle on quantification + . . . 193 computability theory . . . SbC 167 temporal logic (2) + g . . . 435 type theory (2) + . . . . 433 type . . . . . 434 type shifting . . . . Not 23 polymorphism + g . . . 495 substructural logic . . . SbC 200 relevance logic + . . . . 108 entailment + . . . Res 180 Lindstroem's theorem + . . . SbC 481 linear logic . . . 526 variable g . . . . SbC 517 free variable + g . . . Res 179 Goedel's 1st incompleteness theorem (1931) + g . . . SbC 125 feature logic + . . . . 75 unification + . . . 197 model theory (29) . . . . 237 set-theoretic model theory . . . . 11 universal algebra + . . . . 225 infinitary logic . . . . 217 admissible set . . . . 234 recursion-theoretic model theory . . . . 239 ultraproduct . . . . 227 logic with extra quantifiers . . . . SbC 457 modal model theory (7) + . . . . . SbC 215 Kripke semantics + g . . . . . . Not 489 accessability relation + . . . . . Not 461 generated submodel g . . . . . 462 model (4) + . . . . . . SbC 464 finite model g . . . . . . SbC 466 image finite model . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . Par 463 valuation g . . . . . . SbC 465 tree model g . . . . . Not 459 disjoint union of models g . . . . . 455 homomorphism (2) + g . . . . . . SbC 456 bounded homomorphism g . . . . . . SbC 468 bounded morphism . . . . . Not 469 expressive power g . . . . . . Not 470 standard translation + g . . . . . Not 460 bisimulation g . . . . 219 completeness of theories . . . . 235 saturation . . . . 222 equational class . . . . 238 stability . . . . 233 quantifier elimination . . . . 221 denumerable structure . . . . 228 model-theoretic algebra . . . . 236 second-order model theory . . . . 230 model of arithmetic . . . . 218 categoricity g . . . . 220 definability . . . . 226 interpolation . . . . SbC 454 first order model theory . . . . . 455 homomorphism (2) + g . . . . . . SbC 456 bounded homomorphism g . . . . . . SbC 468 bounded morphism . . . . 231 nonclassical model (2) . . . . . 246 sheaf model . . . . . 245 boolean valued . . . . 201 set theory (24) + g . . . . . 398 set-theoretic definability . . . . . Not 391 iota operator . . . . . 384 determinacy . . . . . 387 fuzzy relation . . . . . Not 385 filter . . . . . 389 generalized continuum hypothesis . . . . . 386 function (3) g . . . . . . 482 hypothetical reasoning + . . . . . . 509 functional application . . . . . . 508 functional composition . . . . . Not 394 ordinal definability . . . . . Not 107 consistency + . . . . . 397 set algebra . . . . . 399 Suslin scheme . . . . . SbC 383 descriptive set theory g . . . . . 388 fuzzy set g . . . . . 378 borel classification g . . . . . SbC 380 combinatorial set theory . . . . . Not 390 independence . . . . . 381 constructibility . . . . . 396 relation g . . . . . 377 axiom of choice g . . . . . 392 large cardinal . . . . . Not 395 ordinal number . . . . . 393 Martin's axiom . . . . . 382 continuum hypothesis g . . . . . Not 379 cardinal number . . . . 232 preservation . . . . 216 abstract model theory + . . . . . 254 quantifier (5) + g . . . . . . Not 516 bound variable + g . . . . . . His 514 Frege on quantification + g . . . . . . Not 517 free variable + g . . . . . . His 513 Aristotle on quantification + . . . . . . Not 301 scope . . . . . . . 351 scoping algorithm . . . . 229 model-theoretic forcing . . . . 224 higher-order model theory . . . . Par 493 correspondence theory . . . . 223 finite structure . . . Res 182 Loewenheim-Skolem-Tarski theorem + . . . Not 83 completeness (2) + g . . . . SbC 84 axiomatic completeness . . . . SbC 85 functional completeness + . . . SbC 156 modal logic (13) + g . . . . Ins 512 S4 . . . . 488 modes . . . . 486 frame (2) . . . . . SbC 487 frame constraints . . . . Par 210 modal operator (2) + g . . . . . SbC 472 diamond g . . . . . SbC 473 box g . . . . SbC 213 doxastic logic g . . . . Not 489 accessability relation + . . . . Par 471 modal language (2) g . . . . . Par 210 modal operator (2) + g . . . . . . SbC 472 diamond g . . . . . . SbC 473 box g . . . . . 490 boolean operators . . . . SbC 211 alethic logic g . . . . SbC 212 deontic logic (3) g . . . . . SbC 521 standard deontic logic g . . . . . SbC 523 two-sorted deontic logic g . . . . . SbC 522 dyadic deontic logic g . . . . Par 215 Kripke semantics + g . . . . . Not 489 accessability relation + . . . . Par 457 modal model theory (7) + . . . . . SbC 215 Kripke semantics + g . . . . . . Not 489 accessability relation + . . . . . Not 461 generated submodel g . . . . . 462 model (4) + . . . . . . SbC 464 finite model g . . . . . . SbC 466 image finite model . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . Par 463 valuation g . . . . . . SbC 465 tree model g . . . . . Not 459 disjoint union of models g . . . . . 455 homomorphism (2) + g . . . . . . SbC 456 bounded homomorphism g . . . . . . SbC 468 bounded morphism . . . . . Not 469 expressive power g . . . . . . Not 470 standard translation + g . . . . . Not 460 bisimulation g . . . . SbC 214 epistemic logic g . . . . Not 462 model (4) + . . . . . SbC 464 finite model g . . . . . SbC 466 image finite model . . . . . . Res 467 Hennessy-Milner theorem g . . . . . Par 463 valuation g . . . . . SbC 465 tree model g . . . 194 computational logic (2) . . . Not 183 operator (4) + g . . . . 254 quantifier (5) + g . . . . . Not 516 bound variable + g . . . . . His 514 Frege on quantification + g . . . . . Not 517 free variable + g . . . . . His 513 Aristotle on quantification + . . . . . Not 301 scope . . . . . . 351 scoping algorithm . . . . SbC 210 modal operator (2) + g . . . . . SbC 472 diamond g . . . . . SbC 473 box g . . . . 518 truth-funcional operator (2) g . . . . . SbC 252 iff g . . . . . SbC 253 negation . . . . Not 525 arity g . . . SbC 192 combinatory logic g . . . Par 199 recursive function theory . . . 361 formal semantics (10) + g . . . . 365 property theory . . . . 240 Montague grammar (4) . . . . . 243 sense 243 (4) g . . . . . . 203 meaning relation (5) . . . . . . . 205 hyponymy g . . . . . . . 204 antonymy g . . . . . . . 207 synonymy g . . . . . . . . 149 intensional isomorphism + . . . . . . . 206 paraphrase g . . . . . . . 108 entailment + . . . . . . 375 metaphor g . . . . . . 376 metonymy g . . . . . . 374 literal meaning . . . . . 244 sense 244 g . . . . . 241 meaning postulate . . . . . 242 ptq g . . . . . . 300 quantifying in . . . . 254 quantifier (5) + g . . . . . Not 516 bound variable + g . . . . . His 514 Frege on quantification + g . . . . . Not 517 free variable + g . . . . . His 513 Aristotle on quantification + . . . . . Not 301 scope . . . . . . 351 scoping algorithm . . . . 353 truth (4) + . . . . . 431 truth definition g . . . . . 432 truth value . . . . . 372 truth function + g . . . . . 430 truth condition . . . . 362 dynamic semantics . . . . 363 lexical semantics . . . . 366 situation semantics (2) g . . . . . 402 partiality . . . . . 400 situation . . . . . . 401 scene . . . . Not 507 compositionality . . . . 364 natural logic + . . . . Par 515 quantification (4) + . . . . . Not 516 bound variable + g . . . . . His 514 Frege on quantification + g . . . . . Not 517 free variable + g . . . . . His 513 Aristotle on quantification + . . . SbC 168 lambda calculus (4) g . . . . 170 application . . . . 172 lambda operator . . . . 169 abstraction . . . . 171 conversion . . . 38 knowledge representation (20) + g . . . . 152 frame (1) . . . . 104 database + g . . . . . 105 query g . . . . 165 situation calculus . . . . 167 temporal logic (2) + g . . . . 166 temporal logic (1) g . . . . 93 concept formation . . . . . 90 concept + . . . . . . 91 individual concept . . . . 154 logical omniscience . . . . 162 rule-based representation . . . . 157 predicate logic + g . . . . 159 procedural representation . . . . 161 representation language . . . . 156 modal logic (13) + g . . . . . Ins 512 S4 . . . . . 488 modes . . . . . 486 frame (2) . . . . . . SbC 487 frame constraints . . . . . Par 210 modal operator (2) + g . . . . . . SbC 472 diamond g . . . . . . SbC 473 box g . . . . . SbC 213 doxastic logic g . . . . . Not 489 accessability relation + . . . . . Par 471 modal language (2) g . . . . . . Par 210 modal operator (2) + g . . . . . . . SbC 472 diamond g . . . . . . . SbC 473 box g . . . . . . 490 boolean operators . . . . . SbC 211 alethic logic g . . . . . SbC 212 deontic logic (3) g . . . . . . SbC 521 standard deontic logic g . . . . . . SbC 523 two-sorted deontic logic g . . . . . . SbC 522 dyadic deontic logic g . . . . . Par 215 Kripke semantics + g . . . . . . Not 489 accessability relation + . . . . . Par 457 modal model theory (7) + . . . . . . SbC 215 Kripke semantics + g . . . . . . . Not 489 accessability relation + . . . . . . Not 461 generated submodel g . . . . . . 462 model (4) + . . . . . . . SbC 464 finite model g . . . . . . . SbC 466 image finite model . . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . . Par 463 valuation g . . . . . . . SbC 465 tree model g . . . . . . Not 459 disjoint union of models g . . . . . . 455 homomorphism (2) + g . . . . . . . SbC 456 bounded homomorphism g . . . . . . . SbC 468 bounded morphism . . . . . . Not 469 expressive power g . . . . . . . Not 470 standard translation + g . . . . . . Not 460 bisimulation g . . . . . SbC 214 epistemic logic g . . . . . Not 462 model (4) + . . . . . . SbC 464 finite model g . . . . . . SbC 466 image finite model . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . Par 463 valuation g . . . . . . SbC 465 tree model g . . . . 97 context (2) . . . . . 99 context dependence . . . . . 98 context change . . . . 160 relation system . . . . 153 frame problem g . . . . 92 concept analysis . . . . . 90 concept + . . . . . . 91 individual concept . . . . 163 script . . . . 145 idea g . . . . . 90 concept + . . . . . . 91 individual concept . . . . 164 semantic network g . . . . 247 nonmonotonic logic + g . . . . . 248 default inference . . . Par 367 semantics 367 (8) g . . . . 371 truth conditional semantics . . . . 373 truth table . . . . SbC 215 Kripke semantics + g . . . . . Not 489 accessability relation + . . . . 85 functional completeness + . . . . 370 satisfaction . . . . 369 material implication g . . . . 368 assignment . . . . Not 372 truth function + g . . . Par 201 set theory (24) + g . . . . 398 set-theoretic definability . . . . Not 391 iota operator . . . . 384 determinacy . . . . 387 fuzzy relation . . . . Not 385 filter . . . . 389 generalized continuum hypothesis . . . . 386 function (3) g . . . . . 482 hypothetical reasoning + . . . . . 509 functional application . . . . . 508 functional composition . . . . Not 394 ordinal definability . . . . Not 107 consistency + . . . . 397 set algebra . . . . 399 Suslin scheme . . . . SbC 383 descriptive set theory g . . . . 388 fuzzy set g . . . . 378 borel classification g . . . . SbC 380 combinatorial set theory . . . . Not 390 independence . . . . 381 constructibility . . . . 396 relation g . . . . 377 axiom of choice g . . . . 392 large cardinal . . . . Not 395 ordinal number . . . . 393 Martin's axiom . . . . 382 continuum hypothesis g . . . . Not 379 cardinal number . . . Par 216 abstract model theory + . . . . 254 quantifier (5) + g . . . . . Not 516 bound variable + g . . . . . His 514 Frege on quantification + g . . . . . Not 517 free variable + g . . . . . His 513 Aristotle on quantification + . . . . . Not 301 scope . . . . . . 351 scoping algorithm . . . 178 compactness + . . . His 177 aristotelean logic (2) + g . . . . Par 39 syllogism g . . . . Par 513 Aristotle on quantification + . . . Par 196 foundations of theories . . . 195 constraint programming . . Not 88 software (2) . . . 104 database + g . . . . 105 query g . . . 275 programming language (3) . . . . 190 semantics 190 (8) + g . . . . . 356 denotational semantics . . . . . 119 domain theory g . . . . . . 120 domain . . . . . 360 program analysis . . . . . 359 process model . . . . . SbC 215 Kripke semantics + g . . . . . . Not 489 accessability relation + . . . . . 357 operational semantics . . . . . 358 partial evaluation . . . . . 355 algebraic semantics . . . . 276 syntax 276 . . . . 277 prolog g . . . . . 70 resolution (7) + . . . . . . 339 purity principle . . . . . . 342 simplification . . . . . . 337 demodulation . . . . . . 338 ordering . . . . . . 340 removal of tautologies . . . . . . 341 resolution refinement (4) . . . . . . . 345 lock resolution . . . . . . . 344 hyper resolution . . . . . . . 347 theory resolution . . . . . . . 346 set of support . . . . . . 343 subsumption . . Par 34 artificial intelligence (5) g . . . Par 38 knowledge representation (20) + g . . . . 152 frame (1) . . . . 104 database + g . . . . . 105 query g . . . . 165 situation calculus . . . . 167 temporal logic (2) + g . . . . 166 temporal logic (1) g . . . . 93 concept formation . . . . . 90 concept + . . . . . . 91 individual concept . . . . 154 logical omniscience . . . . 162 rule-based representation . . . . 157 predicate logic + g . . . . 159 procedural representation . . . . 161 representation language . . . . 156 modal logic (13) + g . . . . . Ins 512 S4 . . . . . 488 modes . . . . . 486 frame (2) . . . . . . SbC 487 frame constraints . . . . . Par 210 modal operator (2) + g . . . . . . SbC 472 diamond g . . . . . . SbC 473 box g . . . . . SbC 213 doxastic logic g . . . . . Not 489 accessability relation + . . . . . Par 471 modal language (2) g . . . . . . Par 210 modal operator (2) + g . . . . . . . SbC 472 diamond g . . . . . . . SbC 473 box g . . . . . . 490 boolean operators . . . . . SbC 211 alethic logic g . . . . . SbC 212 deontic logic (3) g . . . . . . SbC 521 standard deontic logic g . . . . . . SbC 523 two-sorted deontic logic g . . . . . . SbC 522 dyadic deontic logic g . . . . . Par 215 Kripke semantics + g . . . . . . Not 489 accessability relation + . . . . . Par 457 modal model theory (7) + . . . . . . SbC 215 Kripke semantics + g . . . . . . . Not 489 accessability relation + . . . . . . Not 461 generated submodel g . . . . . . 462 model (4) + . . . . . . . SbC 464 finite model g . . . . . . . SbC 466 image finite model . . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . . Par 463 valuation g . . . . . . . SbC 465 tree model g . . . . . . Not 459 disjoint union of models g . . . . . . 455 homomorphism (2) + g . . . . . . . SbC 456 bounded homomorphism g . . . . . . . SbC 468 bounded morphism . . . . . . Not 469 expressive power g . . . . . . . Not 470 standard translation + g . . . . . . Not 460 bisimulation g . . . . . SbC 214 epistemic logic g . . . . . Not 462 model (4) + . . . . . . SbC 464 finite model g . . . . . . SbC 466 image finite model . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . Par 463 valuation g . . . . . . SbC 465 tree model g . . . . 97 context (2) . . . . . 99 context dependence . . . . . 98 context change . . . . 160 relation system . . . . 153 frame problem g . . . . 92 concept analysis . . . . . 90 concept + . . . . . . 91 individual concept . . . . 163 script . . . . 145 idea g . . . . . 90 concept + . . . . . . 91 individual concept . . . . 164 semantic network g . . . . 247 nonmonotonic logic + g . . . . . 248 default inference . . . 191 logic (1) (31) + g . . . . Par 53 automated reasoning (25) + . . . . . 35 belief revision . . . . . . 76 update . . . . . 67 nonmonotonic reasoning . . . . . 63 mathematical induction . . . . . 71 rewrite system (3) . . . . . . 350 termination . . . . . . 348 confluence . . . . . . 349 critical pair . . . . . 70 resolution (7) + . . . . . . 339 purity principle . . . . . . 342 simplification . . . . . . 337 demodulation . . . . . . 338 ordering . . . . . . 340 removal of tautologies . . . . . . 341 resolution refinement (4) . . . . . . . 345 lock resolution . . . . . . . 344 hyper resolution . . . . . . . 347 theory resolution . . . . . . . 346 set of support . . . . . . 343 subsumption . . . . . 68 paramodulation . . . . . Not 72 skolemisation . . . . . 65 model checking . . . . . 55 clause 55 (2) . . . . . . 80 horn clause g . . . . . . 79 Gentzen clause . . . . . 74 uncertainty . . . . . 75 unification + . . . . . 57 connection graph procedure . . . . . 64 metatheory . . . . . 61 literal . . . . . 58 connection matrix . . . . . 81 clause 81 . . . . . . SbC 82 relative clause . . . . . 69 reason extraction . . . . . 59 deduction (7) + . . . . . . Not 109 inconsistency . . . . . . 106 consequence g . . . . . . SbC 494 labelled deductive system . . . . . . 111 rule-based deduction . . . . . . Not 108 entailment + . . . . . . 110 natural deduction (2) + g . . . . . . . Not 482 hypothetical reasoning + . . . . . . . Not 483 normalization . . . . . . Not 107 consistency + . . . . . Res 60 Herbrand's theorem . . . . . 56 completion . . . . . . 86 Knuth Bendix completion . . . . . 73 theorem prover (3) . . . . . . 427 Bliksem g . . . . . . 428 Boyer-Moore theorem prover . . . . . . 429 SPASS g . . . . . 66 narrowing . . . . . 62 logic programming g . . . . . 54 answer extraction . . . . . 247 nonmonotonic logic + g . . . . . . 248 default inference . . . . Par 198 proof theory (22) g . . . . . SbC 503 sequent calculus . . . . . . Not 484 structural rules . . . . . 289 interpretation . . . . . 282 constructive analysis . . . . . 295 recursive ordinal . . . . . 287 Goedel numbering . . . . . 288 higher-order arithmetic . . . . . 281 complexity of proofs . . . . . 294 recursive analysis . . . . . Res 292 normal form theorem . . . . . 297 second-order arithmetic . . . . . SbC 110 natural deduction (2) + g . . . . . . Not 482 hypothetical reasoning + . . . . . . Not 483 normalization . . . . . 290 intuitionistic mathematics . . . . . 286 functionals in proof theory . . . . . 298 structure of proofs g . . . . . 283 constructive system . . . . . 291 metamathematics . . . . . 59 deduction (7) + . . . . . . Not 109 inconsistency . . . . . . 106 consequence g . . . . . . SbC 494 labelled deductive system . . . . . . 111 rule-based deduction . . . . . . Not 108 entailment + . . . . . . 110 natural deduction (2) + g . . . . . . . Not 482 hypothetical reasoning + . . . . . . . Not 483 normalization . . . . . . Not 107 consistency + . . . . . 296 relative consistency . . . . . Not 284 cut elimination theorem g . . . . . 293 ordinal notation . . . . . 285 first-order arithmetic . . . . . SbC 485 proof nets . . . . SbC 475 first order logic (4) g . . . . . 254 quantifier (5) + g . . . . . . Not 516 bound variable + g . . . . . . His 514 Frege on quantification + g . . . . . . Not 517 free variable + g . . . . . . His 513 Aristotle on quantification + . . . . . . Not 301 scope . . . . . . . 351 scoping algorithm . . . . . Par 476 first order language g . . . . . . Not 477 fragment (3) g . . . . . . . SbC 479 finite-variable fragment g . . . . . . . SbC 480 guarded fragment g . . . . . . . SbC 478 modal fragment g . . . . . . . . Not 470 standard translation + g . . . . . 511 SPASS g . . . . . Par 515 quantification (4) + . . . . . . Not 516 bound variable + g . . . . . . His 514 Frege on quantification + g . . . . . . Not 517 free variable + g . . . . . . His 513 Aristotle on quantification + . . . . 193 computability theory . . . . SbC 167 temporal logic (2) + g . . . . 435 type theory (2) + . . . . . 433 type . . . . . . 434 type shifting . . . . . Not 23 polymorphism + g . . . . 495 substructural logic . . . . SbC 200 relevance logic + . . . . . 108 entailment + . . . . Res 180 Lindstroem's theorem + . . . . SbC 481 linear logic . . . . 526 variable g . . . . . SbC 517 free variable + g . . . . Res 179 Goedel's 1st incompleteness theorem (1931) + g . . . . SbC 125 feature logic + . . . . . 75 unification + . . . . 197 model theory (29) . . . . . 237 set-theoretic model theory . . . . . 11 universal algebra + . . . . . 225 infinitary logic . . . . . 217 admissible set . . . . . 234 recursion-theoretic model theory . . . . . 239 ultraproduct . . . . . 227 logic with extra quantifiers . . . . . SbC 457 modal model theory (7) + . . . . . . SbC 215 Kripke semantics + g . . . . . . . Not 489 accessability relation + . . . . . . Not 461 generated submodel g . . . . . . 462 model (4) + . . . . . . . SbC 464 finite model g . . . . . . . SbC 466 image finite model . . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . . Par 463 valuation g . . . . . . . SbC 465 tree model g . . . . . . Not 459 disjoint union of models g . . . . . . 455 homomorphism (2) + g . . . . . . . SbC 456 bounded homomorphism g . . . . . . . SbC 468 bounded morphism . . . . . . Not 469 expressive power g . . . . . . . Not 470 standard translation + g . . . . . . Not 460 bisimulation g . . . . . 219 completeness of theories . . . . . 235 saturation . . . . . 222 equational class . . . . . 238 stability . . . . . 233 quantifier elimination . . . . . 221 denumerable structure . . . . . 228 model-theoretic algebra . . . . . 236 second-order model theory . . . . . 230 model of arithmetic . . . . . 218 categoricity g . . . . . 220 definability . . . . . 226 interpolation . . . . . SbC 454 first order model theory . . . . . . 455 homomorphism (2) + g . . . . . . . SbC 456 bounded homomorphism g . . . . . . . SbC 468 bounded morphism . . . . . 231 nonclassical model (2) . . . . . . 246 sheaf model . . . . . . 245 boolean valued . . . . . 201 set theory (24) + g . . . . . . 398 set-theoretic definability . . . . . . Not 391 iota operator . . . . . . 384 determinacy . . . . . . 387 fuzzy relation . . . . . . Not 385 filter . . . . . . 389 generalized continuum hypothesis . . . . . . 386 function (3) g . . . . . . . 482 hypothetical reasoning + . . . . . . . 509 functional application . . . . . . . 508 functional composition . . . . . . Not 394 ordinal definability . . . . . . Not 107 consistency + . . . . . . 397 set algebra . . . . . . 399 Suslin scheme . . . . . . SbC 383 descriptive set theory g . . . . . . 388 fuzzy set g . . . . . . 378 borel classification g . . . . . . SbC 380 combinatorial set theory . . . . . . Not 390 independence . . . . . . 381 constructibility . . . . . . 396 relation g . . . . . . 377 axiom of choice g . . . . . . 392 large cardinal . . . . . . Not 395 ordinal number . . . . . . 393 Martin's axiom . . . . . . 382 continuum hypothesis g . . . . . . Not 379 cardinal number . . . . . 232 preservation . . . . . 216 abstract model theory + . . . . . . 254 quantifier (5) + g . . . . . . . Not 516 bound variable + g . . . . . . . His 514 Frege on quantification + g . . . . . . . Not 517 free variable + g . . . . . . . His 513 Aristotle on quantification + . . . . . . . Not 301 scope . . . . . . . . 351 scoping algorithm . . . . . 229 model-theoretic forcing . . . . . 224 higher-order model theory . . . . . Par 493 correspondence theory . . . . . 223 finite structure . . . . Res 182 Loewenheim-Skolem-Tarski theorem + . . . . Not 83 completeness (2) + g . . . . . SbC 84 axiomatic completeness . . . . . SbC 85 functional completeness + . . . . SbC 156 modal logic (13) + g . . . . . Ins 512 S4 . . . . . 488 modes . . . . . 486 frame (2) . . . . . . SbC 487 frame constraints . . . . . Par 210 modal operator (2) + g . . . . . . SbC 472 diamond g . . . . . . SbC 473 box g . . . . . SbC 213 doxastic logic g . . . . . Not 489 accessability relation + . . . . . Par 471 modal language (2) g . . . . . . Par 210 modal operator (2) + g . . . . . . . SbC 472 diamond g . . . . . . . SbC 473 box g . . . . . . 490 boolean operators . . . . . SbC 211 alethic logic g . . . . . SbC 212 deontic logic (3) g . . . . . . SbC 521 standard deontic logic g . . . . . . SbC 523 two-sorted deontic logic g . . . . . . SbC 522 dyadic deontic logic g . . . . . Par 215 Kripke semantics + g . . . . . . Not 489 accessability relation + . . . . . Par 457 modal model theory (7) + . . . . . . SbC 215 Kripke semantics + g . . . . . . . Not 489 accessability relation + . . . . . . Not 461 generated submodel g . . . . . . 462 model (4) + . . . . . . . SbC 464 finite model g . . . . . . . SbC 466 image finite model . . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . . Par 463 valuation g . . . . . . . SbC 465 tree model g . . . . . . Not 459 disjoint union of models g . . . . . . 455 homomorphism (2) + g . . . . . . . SbC 456 bounded homomorphism g . . . . . . . SbC 468 bounded morphism . . . . . . Not 469 expressive power g . . . . . . . Not 470 standard translation + g . . . . . . Not 460 bisimulation g . . . . . SbC 214 epistemic logic g . . . . . Not 462 model (4) + . . . . . . SbC 464 finite model g . . . . . . SbC 466 image finite model . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . Par 463 valuation g . . . . . . SbC 465 tree model g . . . . 194 computational logic (2) . . . . Not 183 operator (4) + g . . . . . 254 quantifier (5) + g . . . . . . Not 516 bound variable + g . . . . . . His 514 Frege on quantification + g . . . . . . Not 517 free variable + g . . . . . . His 513 Aristotle on quantification + . . . . . . Not 301 scope . . . . . . . 351 scoping algorithm . . . . . SbC 210 modal operator (2) + g . . . . . . SbC 472 diamond g . . . . . . SbC 473 box g . . . . . 518 truth-funcional operator (2) g . . . . . . SbC 252 iff g . . . . . . SbC 253 negation . . . . . Not 525 arity g . . . . SbC 192 combinatory logic g . . . . Par 199 recursive function theory . . . . 361 formal semantics (10) + g . . . . . 365 property theory . . . . . 240 Montague grammar (4) . . . . . . 243 sense 243 (4) g . . . . . . . 203 meaning relation (5) . . . . . . . . 205 hyponymy g . . . . . . . . 204 antonymy g . . . . . . . . 207 synonymy g . . . . . . . . . 149 intensional isomorphism + . . . . . . . . 206 paraphrase g . . . . . . . . 108 entailment + . . . . . . . 375 metaphor g . . . . . . . 376 metonymy g . . . . . . . 374 literal meaning . . . . . . 244 sense 244 g . . . . . . 241 meaning postulate . . . . . . 242 ptq g . . . . . . . 300 quantifying in . . . . . 254 quantifier (5) + g . . . . . . Not 516 bound variable + g . . . . . . His 514 Frege on quantification + g . . . . . . Not 517 free variable + g . . . . . . His 513 Aristotle on quantification + . . . . . . Not 301 scope . . . . . . . 351 scoping algorithm . . . . . 353 truth (4) + . . . . . . 431 truth definition g . . . . . . 432 truth value . . . . . . 372 truth function + g . . . . . . 430 truth condition . . . . . 362 dynamic semantics . . . . . 363 lexical semantics . . . . . 366 situation semantics (2) g . . . . . . 402 partiality . . . . . . 400 situation . . . . . . . 401 scene . . . . . Not 507 compositionality . . . . . 364 natural logic + . . . . . Par 515 quantification (4) + . . . . . . Not 516 bound variable + g . . . . . . His 514 Frege on quantification + g . . . . . . Not 517 free variable + g . . . . . . His 513 Aristotle on quantification + . . . . SbC 168 lambda calculus (4) g . . . . . 170 application . . . . . 172 lambda operator . . . . . 169 abstraction . . . . . 171 conversion . . . . 38 knowledge representation (20) + g . . . . . 152 frame (1) . . . . . 104 database + g . . . . . . 105 query g . . . . . 165 situation calculus . . . . . 167 temporal logic (2) + g . . . . . 166 temporal logic (1) g . . . . . 93 concept formation . . . . . . 90 concept + . . . . . . . 91 individual concept . . . . . 154 logical omniscience . . . . . 162 rule-based representation . . . . . 157 predicate logic + g . . . . . 159 procedural representation . . . . . 161 representation language . . . . . 156 modal logic (13) + g . . . . . . Ins 512 S4 . . . . . . 488 modes . . . . . . 486 frame (2) . . . . . . . SbC 487 frame constraints . . . . . . Par 210 modal operator (2) + g . . . . . . . SbC 472 diamond g . . . . . . . SbC 473 box g . . . . . . SbC 213 doxastic logic g . . . . . . Not 489 accessability relation + . . . . . . Par 471 modal language (2) g . . . . . . . Par 210 modal operator (2) + g . . . . . . . . SbC 472 diamond g . . . . . . . . SbC 473 box g . . . . . . . 490 boolean operators . . . . . . SbC 211 alethic logic g . . . . . . SbC 212 deontic logic (3) g . . . . . . . SbC 521 standard deontic logic g . . . . . . . SbC 523 two-sorted deontic logic g . . . . . . . SbC 522 dyadic deontic logic g . . . . . . Par 215 Kripke semantics + g . . . . . . . Not 489 accessability relation + . . . . . . Par 457 modal model theory (7) + . . . . . . . SbC 215 Kripke semantics + g . . . . . . . . Not 489 accessability relation + . . . . . . . Not 461 generated submodel g . . . . . . . 462 model (4) + . . . . . . . . SbC 464 finite model g . . . . . . . . SbC 466 image finite model . . . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . . . Par 463 valuation g . . . . . . . . SbC 465 tree model g . . . . . . . Not 459 disjoint union of models g . . . . . . . 455 homomorphism (2) + g . . . . . . . . SbC 456 bounded homomorphism g . . . . . . . . SbC 468 bounded morphism . . . . . . . Not 469 expressive power g . . . . . . . . Not 470 standard translation + g . . . . . . . Not 460 bisimulation g . . . . . . SbC 214 epistemic logic g . . . . . . Not 462 model (4) + . . . . . . . SbC 464 finite model g . . . . . . . SbC 466 image finite model . . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . . Par 463 valuation g . . . . . . . SbC 465 tree model g . . . . . 97 context (2) . . . . . . 99 context dependence . . . . . . 98 context change . . . . . 160 relation system . . . . . 153 frame problem g . . . . . 92 concept analysis . . . . . . 90 concept + . . . . . . . 91 individual concept . . . . . 163 script . . . . . 145 idea g . . . . . . 90 concept + . . . . . . . 91 individual concept . . . . . 164 semantic network g . . . . . 247 nonmonotonic logic + g . . . . . . 248 default inference . . . . Par 367 semantics 367 (8) g . . . . . 371 truth conditional semantics . . . . . 373 truth table . . . . . SbC 215 Kripke semantics + g . . . . . . Not 489 accessability relation + . . . . . 85 functional completeness + . . . . . 370 satisfaction . . . . . 369 material implication g . . . . . 368 assignment . . . . . Not 372 truth function + g . . . . Par 201 set theory (24) + g . . . . . 398 set-theoretic definability . . . . . Not 391 iota operator . . . . . 384 determinacy . . . . . 387 fuzzy relation . . . . . Not 385 filter . . . . . 389 generalized continuum hypothesis . . . . . 386 function (3) g . . . . . . 482 hypothetical reasoning + . . . . . . 509 functional application . . . . . . 508 functional composition . . . . . Not 394 ordinal definability . . . . . Not 107 consistency + . . . . . 397 set algebra . . . . . 399 Suslin scheme . . . . . SbC 383 descriptive set theory g . . . . . 388 fuzzy set g . . . . . 378 borel classification g . . . . . SbC 380 combinatorial set theory . . . . . Not 390 independence . . . . . 381 constructibility . . . . . 396 relation g . . . . . 377 axiom of choice g . . . . . 392 large cardinal . . . . . Not 395 ordinal number . . . . . 393 Martin's axiom . . . . . 382 continuum hypothesis g . . . . . Not 379 cardinal number . . . . Par 216 abstract model theory + . . . . . 254 quantifier (5) + g . . . . . . Not 516 bound variable + g . . . . . . His 514 Frege on quantification + g . . . . . . Not 517 free variable + g . . . . . . His 513 Aristotle on quantification + . . . . . . Not 301 scope . . . . . . . 351 scoping algorithm . . . . 178 compactness + . . . . His 177 aristotelean logic (2) + g . . . . . Par 39 syllogism g . . . . . Par 513 Aristotle on quantification + . . . . Par 196 foundations of theories . . . . 195 constraint programming . . . 40 planning . . . Not 36 classification . . . Not 37 heuristic g . . Par 89 theory of computation (4) g . . . Par 127 formal language theory (10) g . . . . 128 categorial grammar + . . . . . SbC 528 combinatorial categorial grammar . . . . 131 context free language g . . . . 130 Chomsky hierarchy g . . . . 134 phrase structure grammar . . . . 129 category . . . . 135 recursive language + g . . . . 137 unrestricted language g . . . . 136 regular language . . . . 132 context sensitive language g . . . . 133 feature constraint . . . Par 302 recursion theory (31) g . . . . 306 complexity of computation . . . . 330 undecidability . . . . 328 theory of numerations . . . . 309 effectively presented structure . . . . 314 isol . . . . 307 decidability (2) g . . . . . 474 tree model property g . . . . . 504 subformula property . . . . 322 recursively enumerable degree . . . . 331 word problem . . . . 327 subrecursive hierarchy . . . . 315 post system . . . . 324 recursively enumerable set . . . . 320 recursive function . . . . 318 recursive axiomatizability . . . . 329 thue system . . . . 325 reducibility . . . . 304 automaton . . . . 310 formal grammar . . . . 326 set recursion theory . . . . 303 abstract recursion theory . . . . 323 recursively enumerable language . . . . 305 axiomatic recursion theory . . . . 135 recursive language + g . . . . 313 inductive definability . . . . 316 recursion theory on admissible sets . . . . Not 52 Turing machine + . . . . 308 degrees of sets of sentences . . . . 319 recursive equivalence type . . . . 312 higher type recursion theory . . . . 317 recursion theory on ordinals . . . . 321 recursive relation . . . . 311 hierarchy . . . Par 185 computational logic (1) (8) g . . . . 190 semantics 190 (8) + g . . . . . 356 denotational semantics . . . . . 119 domain theory g . . . . . . 120 domain . . . . . 360 program analysis . . . . . 359 process model . . . . . SbC 215 Kripke semantics + g . . . . . . Not 489 accessability relation + . . . . . 357 operational semantics . . . . . 358 partial evaluation . . . . . 355 algebraic semantics . . . . 189 reasoning about programs . . . . 53 automated reasoning (25) + . . . . . 35 belief revision . . . . . . 76 update . . . . . 67 nonmonotonic reasoning . . . . . 63 mathematical induction . . . . . 71 rewrite system (3) . . . . . . 350 termination . . . . . . 348 confluence . . . . . . 349 critical pair . . . . . 70 resolution (7) + . . . . . . 339 purity principle . . . . . . 342 simplification . . . . . . 337 demodulation . . . . . . 338 ordering . . . . . . 340 removal of tautologies . . . . . . 341 resolution refinement (4) . . . . . . . 345 lock resolution . . . . . . . 344 hyper resolution . . . . . . . 347 theory resolution . . . . . . . 346 set of support . . . . . . 343 subsumption . . . . . 68 paramodulation . . . . . Not 72 skolemisation . . . . . 65 model checking . . . . . 55 clause 55 (2) . . . . . . 80 horn clause g . . . . . . 79 Gentzen clause . . . . . 74 uncertainty . . . . . 75 unification + . . . . . 57 connection graph procedure . . . . . 64 metatheory . . . . . 61 literal . . . . . 58 connection matrix . . . . . 81 clause 81 . . . . . . SbC 82 relative clause . . . . . 69 reason extraction . . . . . 59 deduction (7) + . . . . . . Not 109 inconsistency . . . . . . 106 consequence g . . . . . . SbC 494 labelled deductive system . . . . . . 111 rule-based deduction . . . . . . Not 108 entailment + . . . . . . 110 natural deduction (2) + g . . . . . . . Not 482 hypothetical reasoning + . . . . . . . Not 483 normalization . . . . . . Not 107 consistency + . . . . . Res 60 Herbrand's theorem . . . . . 56 completion . . . . . . 86 Knuth Bendix completion . . . . . 73 theorem prover (3) . . . . . . 427 Bliksem g . . . . . . 428 Boyer-Moore theorem prover . . . . . . 429 SPASS g . . . . . 66 narrowing . . . . . 62 logic programming g . . . . . 54 answer extraction . . . . . 247 nonmonotonic logic + g . . . . . . 248 default inference . . . . Not 83 completeness (2) + g . . . . . SbC 84 axiomatic completeness . . . . . SbC 85 functional completeness + . . . . 188 program verification (4) . . . . . 274 mechanical verification . . . . . 269 invariant + . . . . . 273 logic of programs . . . . . 43 assertion (2) + . . . . . . 45 imperative assertion . . . . . . 44 declarative assertion . . . . 435 type theory (2) + . . . . . 433 type . . . . . . 434 type shifting . . . . . Not 23 polymorphism + g . . . . 186 program construct (5) . . . . . 265 functional construct . . . . . 267 program scheme . . . . . 266 object oriented construct . . . . . 264 control primitive . . . . . 268 type structure . . . . 187 program specification (5) . . . . . 271 pre-condition . . . . . 269 invariant + . . . . . 272 specification technique . . . . . 43 assertion (2) + . . . . . . 45 imperative assertion . . . . . . 44 declarative assertion . . . . . 270 post-condition . . . Par 48 automata theory (4) . . . . Not 52 Turing machine + . . . . 50 linear bounded automaton . . . . 49 finite state machine g . . . . 51 push down automaton . 173 linguistics (13) g . . Par 446 descriptive linguistics g . . . 142 grammar (5) g . . . . Not 519 derivation g . . . . 452 grammatical constituent g . . . . . 121 ellipsis g . . . . . . 122 antecedent of ellipsis . . . . 444 linguistic unit (3) g . . . . . SbC 440 word (5) g . . . . . . 28 anaphor (2) g . . . . . . . 30 antecedent of an anaphor . . . . . . . 29 anaphora resolution . . . . . . 278 pronoun (2) g . . . . . . . 280 pronoun resolution . . . . . . . 279 demonstrative g . . . . . . 138 function word (2) g . . . . . . . SbC 139 determiner g . . . . . . . SbC 441 modifier g . . . . . . . . 445 adjective (4) g . . . . . . . . . 4 predicative position . . . . . . . . . 1 adverbial modification g . . . . . . . . . 3 intersective adjective . . . . . . . . . 2 graded adjective . . . . . . 442 content word g . . . . . . 425 term (2) g . . . . . . . 426 singular term g . . . . . . . 260 plural term (2) g . . . . . . . . 261 collective reading . . . . . . . . 262 distributive reading . . . . . SbC 500 quantified phrases + . . . . . SbC 115 discourse (3) g . . . . . . 116 discourse particle . . . . . . 118 discourse representation theory g . . . . . . 117 discourse referent . . . . 144 syntax 144 (2) g . . . . . 453 logical syntax g . . . . . . 12 algebraic logic (10) + . . . . . . . 6 boolean algebra + . . . . . . . . SbC 7 boolean algebra with operators . . . . . . . 17 post algebra . . . . . . . 15 Lukasiewicz algebra . . . . . . . 14 cylindric algebra g . . . . . . . 8 lattice + g . . . . . . . 18 quantum logic . . . . . . . 10 relation algebra + . . . . . . . 13 categorical logic . . . . . . . 16 polyadic algebra . . . . . . . 19 topos . . . . . 423 syntactic category (3) g . . . . . . 447 part of speech g . . . . . . SbC 249 noun (2) g . . . . . . . SbC 251 proper name . . . . . . . SbC 250 mass noun g . . . . . . SbC 438 verb g . . . . . . . SbC 439 perception verb . . . . 143 sentence g . . 443 linguistic geography g . . Not 502 discontinuity . . Par 361 formal semantics (10) + g . . . 365 property theory . . . 240 Montague grammar (4) . . . . 243 sense 243 (4) g . . . . . 203 meaning relation (5) . . . . . . 205 hyponymy g . . . . . . 204 antonymy g . . . . . . 207 synonymy g . . . . . . . 149 intensional isomorphism + . . . . . . 206 paraphrase g . . . . . . 108 entailment + . . . . . 375 metaphor g . . . . . 376 metonymy g . . . . . 374 literal meaning . . . . 244 sense 244 g . . . . 241 meaning postulate . . . . 242 ptq g . . . . . 300 quantifying in . . . 254 quantifier (5) + g . . . . Not 516 bound variable + g . . . . His 514 Frege on quantification + g . . . . Not 517 free variable + g . . . . His 513 Aristotle on quantification + . . . . Not 301 scope . . . . . 351 scoping algorithm . . . 353 truth (4) + . . . . 431 truth definition g . . . . 432 truth value . . . . 372 truth function + g . . . . 430 truth condition . . . 362 dynamic semantics . . . 363 lexical semantics . . . 366 situation semantics (2) g . . . . 402 partiality . . . . 400 situation . . . . . 401 scene . . . Not 507 compositionality . . . 364 natural logic + . . . Par 515 quantification (4) + . . . . Not 516 bound variable + g . . . . His 514 Frege on quantification + g . . . . Not 517 free variable + g . . . . His 513 Aristotle on quantification + . . Not 20 ambiguity (7) g . . . SbC 27 syntactic ambiguity . . . SbC 25 semantic ambiguity + g . . . SbC 22 lexical ambiguity g . . . SbC 21 derivational ambiguity . . . SbC 24 pragmatic ambiguity . . . SbC 26 structural ambiguity . . . 23 polymorphism + g . . 510 frameworks (7) . . . 535 LFG . . . 128 categorial grammar + . . . . SbC 528 combinatorial categorial grammar . . . 530 TAG . . . 532 DRT . . . 529 GB . . . 534 HPSG . . . 531 dynamic syntax . . 506 linguistic phenomena . . Not 174 language acquisition g . . Par 450 pragmatics (2) g . . . 403 speech act (5) g . . . . 408 statement (2) g . . . . . 112 description (2) g . . . . . . SbC 114 indefinite description . . . . . . SbC 113 definite description . . . . . 409 indicative statement . . . . 405 indirect speech act . . . . 406 performative . . . . 407 performative hypothesis . . . . 404 illocutionary force . . . 100 conversational maxim (3) g . . . . 103 implicature + g . . . . 102 cooperative principle . . . . 101 conversational implicature g . . 499 syntax and semantic interface + . . Par 175 semantics 175 (16) g . . . 25 semantic ambiguity + g . . . Not 123 extension g . . . . 124 extensionality g . . . 334 referent g . . . Not 332 reference (2) g . . . . 333 identity puzzle . . . . 335 referential term . . . . . SbC 336 anchor . . . Not 263 presupposition g . . . . 103 implicature + g . . . Not 146 indexicality . . . . 147 indexical expression g . . . Par 41 aspect . . . . 42 aspectual classification . . . SbC 361 formal semantics (10) + g . . . . 365 property theory . . . . 240 Montague grammar (4) . . . . . 243 sense 243 (4) g . . . . . . 203 meaning relation (5) . . . . . . . 205 hyponymy g . . . . . . . 204 antonymy g . . . . . . . 207 synonymy g . . . . . . . . 149 intensional isomorphism + . . . . . . . 206 paraphrase g . . . . . . . 108 entailment + . . . . . . 375 metaphor g . . . . . . 376 metonymy g . . . . . . 374 literal meaning . . . . . 244 sense 244 g . . . . . 241 meaning postulate . . . . . 242 ptq g . . . . . . 300 quantifying in . . . . 254 quantifier (5) + g . . . . . Not 516 bound variable + g . . . . . His 514 Frege on quantification + g . . . . . Not 517 free variable + g . . . . . His 513 Aristotle on quantification + . . . . . Not 301 scope . . . . . . 351 scoping algorithm . . . . 353 truth (4) + . . . . . 431 truth definition g . . . . . 432 truth value . . . . . 372 truth function + g . . . . . 430 truth condition . . . . 362 dynamic semantics . . . . 363 lexical semantics . . . . 366 situation semantics (2) g . . . . . 402 partiality . . . . . 400 situation . . . . . . 401 scene . . . . Not 507 compositionality . . . . 364 natural logic + . . . . Par 515 quantification (4) + . . . . . Not 516 bound variable + g . . . . . His 514 Frege on quantification + g . . . . . Not 517 free variable + g . . . . . His 513 Aristotle on quantification + . . . Not 501 coordination . . . Not 353 truth (4) + . . . . 431 truth definition g . . . . 432 truth value . . . . 372 truth function + g . . . . 430 truth condition . . . Not 354 underspecification (2) . . . . 437 quasi-logical form . . . . 436 monotonic semantics . . . 499 syntax and semantic interface + . . . Par 46 attitude . . . . SbC 47 propositional attitude . . . . . Not 299 belief . . . Not 500 quantified phrases + . . . Not 148 intension (3) g . . . . 149 intensional isomorphism + . . . . 151 intensionality . . . . 150 intensional verb . . . 31 animal (3) g . . . . SbC 33 unicorn . . . . SbC 32 donkey . . . . SbC 352 rabbit . . Par 496 syntax 496 (2) g . . . Par 498 word order . . . Par 497 movement . . Par 140 language generation . . . 141 reversibility . 202 mathematics (5) g . . Not 527 algebra 2 g . . 191 logic (1) (31) + g . . . Par 53 automated reasoning (25) + . . . . 35 belief revision . . . . . 76 update . . . . 67 nonmonotonic reasoning . . . . 63 mathematical induction . . . . 71 rewrite system (3) . . . . . 350 termination . . . . . 348 confluence . . . . . 349 critical pair . . . . 70 resolution (7) + . . . . . 339 purity principle . . . . . 342 simplification . . . . . 337 demodulation . . . . . 338 ordering . . . . . 340 removal of tautologies . . . . . 341 resolution refinement (4) . . . . . . 345 lock resolution . . . . . . 344 hyper resolution . . . . . . 347 theory resolution . . . . . . 346 set of support . . . . . 343 subsumption . . . . 68 paramodulation . . . . Not 72 skolemisation . . . . 65 model checking . . . . 55 clause 55 (2) . . . . . 80 horn clause g . . . . . 79 Gentzen clause . . . . 74 uncertainty . . . . 75 unification + . . . . 57 connection graph procedure . . . . 64 metatheory . . . . 61 literal . . . . 58 connection matrix . . . . 81 clause 81 . . . . . SbC 82 relative clause . . . . 69 reason extraction . . . . 59 deduction (7) + . . . . . Not 109 inconsistency . . . . . 106 consequence g . . . . . SbC 494 labelled deductive system . . . . . 111 rule-based deduction . . . . . Not 108 entailment + . . . . . 110 natural deduction (2) + g . . . . . . Not 482 hypothetical reasoning + . . . . . . Not 483 normalization . . . . . Not 107 consistency + . . . . Res 60 Herbrand's theorem . . . . 56 completion . . . . . 86 Knuth Bendix completion . . . . 73 theorem prover (3) . . . . . 427 Bliksem g . . . . . 428 Boyer-Moore theorem prover . . . . . 429 SPASS g . . . . 66 narrowing . . . . 62 logic programming g . . . . 54 answer extraction . . . . 247 nonmonotonic logic + g . . . . . 248 default inference . . . Par 198 proof theory (22) g . . . . SbC 503 sequent calculus . . . . . Not 484 structural rules . . . . 289 interpretation . . . . 282 constructive analysis . . . . 295 recursive ordinal . . . . 287 Goedel numbering . . . . 288 higher-order arithmetic . . . . 281 complexity of proofs . . . . 294 recursive analysis . . . . Res 292 normal form theorem . . . . 297 second-order arithmetic . . . . SbC 110 natural deduction (2) + g . . . . . Not 482 hypothetical reasoning + . . . . . Not 483 normalization . . . . 290 intuitionistic mathematics . . . . 286 functionals in proof theory . . . . 298 structure of proofs g . . . . 283 constructive system . . . . 291 metamathematics . . . . 59 deduction (7) + . . . . . Not 109 inconsistency . . . . . 106 consequence g . . . . . SbC 494 labelled deductive system . . . . . 111 rule-based deduction . . . . . Not 108 entailment + . . . . . 110 natural deduction (2) + g . . . . . . Not 482 hypothetical reasoning + . . . . . . Not 483 normalization . . . . . Not 107 consistency + . . . . 296 relative consistency . . . . Not 284 cut elimination theorem g . . . . 293 ordinal notation . . . . 285 first-order arithmetic . . . . SbC 485 proof nets . . . SbC 475 first order logic (4) g . . . . 254 quantifier (5) + g . . . . . Not 516 bound variable + g . . . . . His 514 Frege on quantification + g . . . . . Not 517 free variable + g . . . . . His 513 Aristotle on quantification + . . . . . Not 301 scope . . . . . . 351 scoping algorithm . . . . Par 476 first order language g . . . . . Not 477 fragment (3) g . . . . . . SbC 479 finite-variable fragment g . . . . . . SbC 480 guarded fragment g . . . . . . SbC 478 modal fragment g . . . . . . . Not 470 standard translation + g . . . . 511 SPASS g . . . . Par 515 quantification (4) + . . . . . Not 516 bound variable + g . . . . . His 514 Frege on quantification + g . . . . . Not 517 free variable + g . . . . . His 513 Aristotle on quantification + . . . 193 computability theory . . . SbC 167 temporal logic (2) + g . . . 435 type theory (2) + . . . . 433 type . . . . . 434 type shifting . . . . Not 23 polymorphism + g . . . 495 substructural logic . . . SbC 200 relevance logic + . . . . 108 entailment + . . . Res 180 Lindstroem's theorem + . . . SbC 481 linear logic . . . 526 variable g . . . . SbC 517 free variable + g . . . Res 179 Goedel's 1st incompleteness theorem (1931) + g . . . SbC 125 feature logic + . . . . 75 unification + . . . 197 model theory (29) . . . . 237 set-theoretic model theory . . . . 11 universal algebra + . . . . 225 infinitary logic . . . . 217 admissible set . . . . 234 recursion-theoretic model theory . . . . 239 ultraproduct . . . . 227 logic with extra quantifiers . . . . SbC 457 modal model theory (7) + . . . . . SbC 215 Kripke semantics + g . . . . . . Not 489 accessability relation + . . . . . Not 461 generated submodel g . . . . . 462 model (4) + . . . . . . SbC 464 finite model g . . . . . . SbC 466 image finite model . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . Par 463 valuation g . . . . . . SbC 465 tree model g . . . . . Not 459 disjoint union of models g . . . . . 455 homomorphism (2) + g . . . . . . SbC 456 bounded homomorphism g . . . . . . SbC 468 bounded morphism . . . . . Not 469 expressive power g . . . . . . Not 470 standard translation + g . . . . . Not 460 bisimulation g . . . . 219 completeness of theories . . . . 235 saturation . . . . 222 equational class . . . . 238 stability . . . . 233 quantifier elimination . . . . 221 denumerable structure . . . . 228 model-theoretic algebra . . . . 236 second-order model theory . . . . 230 model of arithmetic . . . . 218 categoricity g . . . . 220 definability . . . . 226 interpolation . . . . SbC 454 first order model theory . . . . . 455 homomorphism (2) + g . . . . . . SbC 456 bounded homomorphism g . . . . . . SbC 468 bounded morphism . . . . 231 nonclassical model (2) . . . . . 246 sheaf model . . . . . 245 boolean valued . . . . 201 set theory (24) + g . . . . . 398 set-theoretic definability . . . . . Not 391 iota operator . . . . . 384 determinacy . . . . . 387 fuzzy relation . . . . . Not 385 filter . . . . . 389 generalized continuum hypothesis . . . . . 386 function (3) g . . . . . . 482 hypothetical reasoning + . . . . . . 509 functional application . . . . . . 508 functional composition . . . . . Not 394 ordinal definability . . . . . Not 107 consistency + . . . . . 397 set algebra . . . . . 399 Suslin scheme . . . . . SbC 383 descriptive set theory g . . . . . 388 fuzzy set g . . . . . 378 borel classification g . . . . . SbC 380 combinatorial set theory . . . . . Not 390 independence . . . . . 381 constructibility . . . . . 396 relation g . . . . . 377 axiom of choice g . . . . . 392 large cardinal . . . . . Not 395 ordinal number . . . . . 393 Martin's axiom . . . . . 382 continuum hypothesis g . . . . . Not 379 cardinal number . . . . 232 preservation . . . . 216 abstract model theory + . . . . . 254 quantifier (5) + g . . . . . . Not 516 bound variable + g . . . . . . His 514 Frege on quantification + g . . . . . . Not 517 free variable + g . . . . . . His 513 Aristotle on quantification + . . . . . . Not 301 scope . . . . . . . 351 scoping algorithm . . . . 229 model-theoretic forcing . . . . 224 higher-order model theory . . . . Par 493 correspondence theory . . . . 223 finite structure . . . Res 182 Loewenheim-Skolem-Tarski theorem + . . . Not 83 completeness (2) + g . . . . SbC 84 axiomatic completeness . . . . SbC 85 functional completeness + . . . SbC 156 modal logic (13) + g . . . . Ins 512 S4 . . . . 488 modes . . . . 486 frame (2) . . . . . SbC 487 frame constraints . . . . Par 210 modal operator (2) + g . . . . . SbC 472 diamond g . . . . . SbC 473 box g . . . . SbC 213 doxastic logic g . . . . Not 489 accessability relation + . . . . Par 471 modal language (2) g . . . . . Par 210 modal operator (2) + g . . . . . . SbC 472 diamond g . . . . . . SbC 473 box g . . . . . 490 boolean operators . . . . SbC 211 alethic logic g . . . . SbC 212 deontic logic (3) g . . . . . SbC 521 standard deontic logic g . . . . . SbC 523 two-sorted deontic logic g . . . . . SbC 522 dyadic deontic logic g . . . . Par 215 Kripke semantics + g . . . . . Not 489 accessability relation + . . . . Par 457 modal model theory (7) + . . . . . SbC 215 Kripke semantics + g . . . . . . Not 489 accessability relation + . . . . . Not 461 generated submodel g . . . . . 462 model (4) + . . . . . . SbC 464 finite model g . . . . . . SbC 466 image finite model . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . Par 463 valuation g . . . . . . SbC 465 tree model g . . . . . Not 459 disjoint union of models g . . . . . 455 homomorphism (2) + g . . . . . . SbC 456 bounded homomorphism g . . . . . . SbC 468 bounded morphism . . . . . Not 469 expressive power g . . . . . . Not 470 standard translation + g . . . . . Not 460 bisimulation g . . . . SbC 214 epistemic logic g . . . . Not 462 model (4) + . . . . . SbC 464 finite model g . . . . . SbC 466 image finite model . . . . . . Res 467 Hennessy-Milner theorem g . . . . . Par 463 valuation g . . . . . SbC 465 tree model g . . . 194 computational logic (2) . . . Not 183 operator (4) + g . . . . 254 quantifier (5) + g . . . . . Not 516 bound variable + g . . . . . His 514 Frege on quantification + g . . . . . Not 517 free variable + g . . . . . His 513 Aristotle on quantification + . . . . . Not 301 scope . . . . . . 351 scoping algorithm . . . . SbC 210 modal operator (2) + g . . . . . SbC 472 diamond g . . . . . SbC 473 box g . . . . 518 truth-funcional operator (2) g . . . . . SbC 252 iff g . . . . . SbC 253 negation . . . . Not 525 arity g . . . SbC 192 combinatory logic g . . . Par 199 recursive function theory . . . 361 formal semantics (10) + g . . . . 365 property theory . . . . 240 Montague grammar (4) . . . . . 243 sense 243 (4) g . . . . . . 203 meaning relation (5) . . . . . . . 205 hyponymy g . . . . . . . 204 antonymy g . . . . . . . 207 synonymy g . . . . . . . . 149 intensional isomorphism + . . . . . . . 206 paraphrase g . . . . . . . 108 entailment + . . . . . . 375 metaphor g . . . . . . 376 metonymy g . . . . . . 374 literal meaning . . . . . 244 sense 244 g . . . . . 241 meaning postulate . . . . . 242 ptq g . . . . . . 300 quantifying in . . . . 254 quantifier (5) + g . . . . . Not 516 bound variable + g . . . . . His 514 Frege on quantification + g . . . . . Not 517 free variable + g . . . . . His 513 Aristotle on quantification + . . . . . Not 301 scope . . . . . . 351 scoping algorithm . . . . 353 truth (4) + . . . . . 431 truth definition g . . . . . 432 truth value . . . . . 372 truth function + g . . . . . 430 truth condition . . . . 362 dynamic semantics . . . . 363 lexical semantics . . . . 366 situation semantics (2) g . . . . . 402 partiality . . . . . 400 situation . . . . . . 401 scene . . . . Not 507 compositionality . . . . 364 natural logic + . . . . Par 515 quantification (4) + . . . . . Not 516 bound variable + g . . . . . His 514 Frege on quantification + g . . . . . Not 517 free variable + g . . . . . His 513 Aristotle on quantification + . . . SbC 168 lambda calculus (4) g . . . . 170 application . . . . 172 lambda operator . . . . 169 abstraction . . . . 171 conversion . . . 38 knowledge representation (20) + g . . . . 152 frame (1) . . . . 104 database + g . . . . . 105 query g . . . . 165 situation calculus . . . . 167 temporal logic (2) + g . . . . 166 temporal logic (1) g . . . . 93 concept formation . . . . . 90 concept + . . . . . . 91 individual concept . . . . 154 logical omniscience . . . . 162 rule-based representation . . . . 157 predicate logic + g . . . . 159 procedural representation . . . . 161 representation language . . . . 156 modal logic (13) + g . . . . . Ins 512 S4 . . . . . 488 modes . . . . . 486 frame (2) . . . . . . SbC 487 frame constraints . . . . . Par 210 modal operator (2) + g . . . . . . SbC 472 diamond g . . . . . . SbC 473 box g . . . . . SbC 213 doxastic logic g . . . . . Not 489 accessability relation + . . . . . Par 471 modal language (2) g . . . . . . Par 210 modal operator (2) + g . . . . . . . SbC 472 diamond g . . . . . . . SbC 473 box g . . . . . . 490 boolean operators . . . . . SbC 211 alethic logic g . . . . . SbC 212 deontic logic (3) g . . . . . . SbC 521 standard deontic logic g . . . . . . SbC 523 two-sorted deontic logic g . . . . . . SbC 522 dyadic deontic logic g . . . . . Par 215 Kripke semantics + g . . . . . . Not 489 accessability relation + . . . . . Par 457 modal model theory (7) + . . . . . . SbC 215 Kripke semantics + g . . . . . . . Not 489 accessability relation + . . . . . . Not 461 generated submodel g . . . . . . 462 model (4) + . . . . . . . SbC 464 finite model g . . . . . . . SbC 466 image finite model . . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . . Par 463 valuation g . . . . . . . SbC 465 tree model g . . . . . . Not 459 disjoint union of models g . . . . . . 455 homomorphism (2) + g . . . . . . . SbC 456 bounded homomorphism g . . . . . . . SbC 468 bounded morphism . . . . . . Not 469 expressive power g . . . . . . . Not 470 standard translation + g . . . . . . Not 460 bisimulation g . . . . . SbC 214 epistemic logic g . . . . . Not 462 model (4) + . . . . . . SbC 464 finite model g . . . . . . SbC 466 image finite model . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . Par 463 valuation g . . . . . . SbC 465 tree model g . . . . 97 context (2) . . . . . 99 context dependence . . . . . 98 context change . . . . 160 relation system . . . . 153 frame problem g . . . . 92 concept analysis . . . . . 90 concept + . . . . . . 91 individual concept . . . . 163 script . . . . 145 idea g . . . . . 90 concept + . . . . . . 91 individual concept . . . . 164 semantic network g . . . . 247 nonmonotonic logic + g . . . . . 248 default inference . . . Par 367 semantics 367 (8) g . . . . 371 truth conditional semantics . . . . 373 truth table . . . . SbC 215 Kripke semantics + g . . . . . Not 489 accessability relation + . . . . 85 functional completeness + . . . . 370 satisfaction . . . . 369 material implication g . . . . 368 assignment . . . . Not 372 truth function + g . . . Par 201 set theory (24) + g . . . . 398 set-theoretic definability . . . . Not 391 iota operator . . . . 384 determinacy . . . . 387 fuzzy relation . . . . Not 385 filter . . . . 389 generalized continuum hypothesis . . . . 386 function (3) g . . . . . 482 hypothetical reasoning + . . . . . 509 functional application . . . . . 508 functional composition . . . . Not 394 ordinal definability . . . . Not 107 consistency + . . . . 397 set algebra . . . . 399 Suslin scheme . . . . SbC 383 descriptive set theory g . . . . 388 fuzzy set g . . . . 378 borel classification g . . . . SbC 380 combinatorial set theory . . . . Not 390 independence . . . . 381 constructibility . . . . 396 relation g . . . . 377 axiom of choice g . . . . 392 large cardinal . . . . Not 395 ordinal number . . . . 393 Martin's axiom . . . . 382 continuum hypothesis g . . . . Not 379 cardinal number . . . Par 216 abstract model theory + . . . . 254 quantifier (5) + g . . . . . Not 516 bound variable + g . . . . . His 514 Frege on quantification + g . . . . . Not 517 free variable + g . . . . . His 513 Aristotle on quantification + . . . . . Not 301 scope . . . . . . 351 scoping algorithm . . . 178 compactness + . . . His 177 aristotelean logic (2) + g . . . . Par 39 syllogism g . . . . Par 513 Aristotle on quantification + . . . Par 196 foundations of theories . . . 195 constraint programming . . 424 system g . . Par 5 algebra 1 (8) g . . . 8 lattice + g . . . SbC 6 boolean algebra + . . . . SbC 7 boolean algebra with operators . . . 11 universal algebra + . . . 77 category theory + g . . . . 78 bottom . . . SbC 9 Lindenbaum algebra . . . 10 relation algebra + . . . 12 algebraic logic (10) + . . . . 6 boolean algebra + . . . . . SbC 7 boolean algebra with operators . . . . 17 post algebra . . . . 15 Lukasiewicz algebra . . . . 14 cylindric algebra g . . . . 8 lattice + g . . . . 18 quantum logic . . . . 10 relation algebra + . . . . 13 categorical logic . . . . 16 polyadic algebra . . . . 19 topos . . . Par 491 algebraic principles . . . . SbC 492 residuation . . 176 mathematical logic (12) g . . . Res 180 Lindstroem's theorem + . . . 77 category theory + g . . . . 78 bottom . . . 53 automated reasoning (25) + . . . . 35 belief revision . . . . . 76 update . . . . 67 nonmonotonic reasoning . . . . 63 mathematical induction . . . . 71 rewrite system (3) . . . . . 350 termination . . . . . 348 confluence . . . . . 349 critical pair . . . . 70 resolution (7) + . . . . . 339 purity principle . . . . . 342 simplification . . . . . 337 demodulation . . . . . 338 ordering . . . . . 340 removal of tautologies . . . . . 341 resolution refinement (4) . . . . . . 345 lock resolution . . . . . . 344 hyper resolution . . . . . . 347 theory resolution . . . . . . 346 set of support . . . . . 343 subsumption . . . . 68 paramodulation . . . . Not 72 skolemisation . . . . 65 model checking . . . . 55 clause 55 (2) . . . . . 80 horn clause g . . . . . 79 Gentzen clause . . . . 74 uncertainty . . . . 75 unification + . . . . 57 connection graph procedure . . . . 64 metatheory . . . . 61 literal . . . . 58 connection matrix . . . . 81 clause 81 . . . . . SbC 82 relative clause . . . . 69 reason extraction . . . . 59 deduction (7) + . . . . . Not 109 inconsistency . . . . . 106 consequence g . . . . . SbC 494 labelled deductive system . . . . . 111 rule-based deduction . . . . . Not 108 entailment + . . . . . 110 natural deduction (2) + g . . . . . . Not 482 hypothetical reasoning + . . . . . . Not 483 normalization . . . . . Not 107 consistency + . . . . Res 60 Herbrand's theorem . . . . 56 completion . . . . . 86 Knuth Bendix completion . . . . 73 theorem prover (3) . . . . . 427 Bliksem g . . . . . 428 Boyer-Moore theorem prover . . . . . 429 SPASS g . . . . 66 narrowing . . . . 62 logic programming g . . . . 54 answer extraction . . . . 247 nonmonotonic logic + g . . . . . 248 default inference . . . Res 182 Loewenheim-Skolem-Tarski theorem + . . . 181 logical constants . . . Not 83 completeness (2) + g . . . . SbC 84 axiomatic completeness . . . . SbC 85 functional completeness + . . . Res 179 Goedel's 1st incompleteness theorem (1931) + g . . . Not 183 operator (4) + g . . . . 254 quantifier (5) + g . . . . . Not 516 bound variable + g . . . . . His 514 Frege on quantification + g . . . . . Not 517 free variable + g . . . . . His 513 Aristotle on quantification + . . . . . Not 301 scope . . . . . . 351 scoping algorithm . . . . SbC 210 modal operator (2) + g . . . . . SbC 472 diamond g . . . . . SbC 473 box g . . . . 518 truth-funcional operator (2) g . . . . . SbC 252 iff g . . . . . SbC 253 negation . . . . Not 525 arity g . . . Not 178 compactness + . . . Res 520 Goedel's 2nd incompleteness theorem (1931) g . . . 435 type theory (2) + . . . . 433 type . . . . . 434 type shifting . . . . Not 23 polymorphism + g . . . 184 symbolic logic (18) g . . . . SbC 412 dynamic logic . . . . 420 partial logic . . . . SbC 413 fuzzy logic g . . . . 200 relevance logic + . . . . . 108 entailment + . . . . SbC 419 paraconsistent logic . . . . 416 intermediate logic . . . . 125 feature logic + . . . . . 75 unification + . . . . 157 predicate logic + g . . . . 364 natural logic + . . . . SbC 422 propositional logic g . . . . SbC 410 boolean logic g . . . . SbC 156 modal logic (13) + g . . . . . Ins 512 S4 . . . . . 488 modes . . . . . 486 frame (2) . . . . . . SbC 487 frame constraints . . . . . Par 210 modal operator (2) + g . . . . . . SbC 472 diamond g . . . . . . SbC 473 box g . . . . . SbC 213 doxastic logic g . . . . . Not 489 accessability relation + . . . . . Par 471 modal language (2) g . . . . . . Par 210 modal operator (2) + g . . . . . . . SbC 472 diamond g . . . . . . . SbC 473 box g . . . . . . 490 boolean operators . . . . . SbC 211 alethic logic g . . . . . SbC 212 deontic logic (3) g . . . . . . SbC 521 standard deontic logic g . . . . . . SbC 523 two-sorted deontic logic g . . . . . . SbC 522 dyadic deontic logic g . . . . . Par 215 Kripke semantics + g . . . . . . Not 489 accessability relation + . . . . . Par 457 modal model theory (7) + . . . . . . SbC 215 Kripke semantics + g . . . . . . . Not 489 accessability relation + . . . . . . Not 461 generated submodel g . . . . . . 462 model (4) + . . . . . . . SbC 464 finite model g . . . . . . . SbC 466 image finite model . . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . . Par 463 valuation g . . . . . . . SbC 465 tree model g . . . . . . Not 459 disjoint union of models g . . . . . . 455 homomorphism (2) + g . . . . . . . SbC 456 bounded homomorphism g . . . . . . . SbC 468 bounded morphism . . . . . . Not 469 expressive power g . . . . . . . Not 470 standard translation + g . . . . . . Not 460 bisimulation g . . . . . SbC 214 epistemic logic g . . . . . Not 462 model (4) + . . . . . . SbC 464 finite model g . . . . . . SbC 466 image finite model . . . . . . . Res 467 Hennessy-Milner theorem g . . . . . . Par 463 valuation g . . . . . . SbC 465 tree model g . . . . SbC 418 many-valued logic g . . . . SbC 417 intuitionistic logic g . . . . SbC 421 probability logic . . . . 411 conditional logic . . . . SbC 414 higher-order logic . . . . 415 inductive logic . 258 philosophy (3) g . . Par 524 philosophy of language g . . Par 259 logic 259 (2) g . . . His 177 aristotelean logic (2) + g . . . . Par 39 syllogism g . . . . Par 513 Aristotle on quantification + . . . 449 proposition (2) g . . . . 448 contradiction g . . . . . 255 paradox (2) g . . . . . . 256 liar paradox g . . . . . . 257 semantic paradox . . . . 94 conditional statement (2) . . . . . 95 antecedent . . . . . 96 counterfactual g . . Par 208 metaphysics g . . . 209 common sense world g

33. Qualifying Exam Syllabi formal languages, truth assignments and tautologies, firstorder languages and structures, formal deductions, the completeness theorem, theories and their http://www.math.umd.edu/graduate/exams/syllabi.shtml

HOME PEOPLE UNDERGRADUATE GRADUATE ... Examinations Qualifying Exam Syllabi General Information The purpose of the written qualifying exams, as endorsed by the Policy Committee in Spring 1990, is to indicate that the student has the basic knowledge and mathematical ability to begin advanced study. The Department Written Examination for the Ph.D and M.A. is administered in January and August of each year during the two weeks preceding the first week of classes and is given in the following fields: algebra, analysis, logic, numerical analysis, ... statistics, applied statistics: (PhD level), (MA level), and topology. Six questions must be answered on each part. In some subjects, there will be a separate examination for students seeking the M.A., that will be given at the same time as the Ph.D. examination. The M.A. level examination may cover less material, but some of the questions may be the same as those on the Ph.D. level examination. M.A. students may exercise the option of taking the Ph.D. examination and only being required to receive an "M.A. pass". Each examination will last four hours and no two will be scheduled on consecutive days.

34. Model Theory - Elsevier completeness and Compactness. Refinements of the Method. Omitting Types and Interpolation Theorems. Countable Models of Complete theories. http://129.35.76.177/wps/find/bookdescription.cws_home/502287/description?navope

35. CAT.INIST Its subject looks something like early model theory, and the main result, completeness; Catégoricité; Categoricity; Logicisme; Logicism; Gödel(K. http://cat.inist.fr/?aModele=afficheN&cpsidt=1164729

36. Review Of GIANDOMENICO SICA (ed.) What Is Category Theory? Polimetrica, 2006 « Awodey, S. (2006) Category Theory. Oxford Oxford University Press. Awodey, S. and Reck, E. (2002) “completeness and Categoricity I. NineteenCentury http://johnsymons.wordpress.com/2007/10/24/review-of-giandomenico-sica-ed-what-i

Objects and Arrows Home About Review of GIANDOMENICO SICA (ed.) What is Category Theory? Polimetrica, 2006 October 24, 2007 ANOTHER UPDATE (11/19/07):  THE EDITOR OF THIS BOOK, GIANDOMENICO SICA TELLS ME THAT IT WILL SOON BE AVAILABLE AT AMAZON AND BN.  SO PLEASE DISREGARD MY COMPLAINTS ABOUT AVAILABILITY BELOW. UPDATE: CORRECTED VERSION OF THIS REVIEW IS HERE MANY THANKS TO VLADIK KREINOVICH FOR THE CORRECTIONS AND CRITICISMS! A FINISHED VERSION WILL APPEAR IN STUDIA LOGICA. Giandomenico Sica’s volume is a collection of eleven papers on category theory by philosophers, mathematicians, and mathematical physicists. In addition to papers of direct interest to philosophers of mathematics, the volume contains some introductory expositions of category theory along with a valuable discussion of the relationship between category theory and physics by Bob Coecke. While there are several technically difficult papers, the volume as a whole is reasonably accessible to those with some familiarity with the basics of category theory. The importance of the volume lies in the possibility that it will encourage broader interest in category theory among philosophers.

37. Courses In The Department Of Mathematics completeness and compactness; elimination of quantifiers; omission of types; Model Theory II Saturated models; Categoricity in power; CantorBendixson http://catalogs.uchicago.edu/divisions/math-courses.html

Courses in the Department of Mathematics Courses 30000, 30100. Set Theory I,II Hirschfeldt 30200. Computability Theory I (Ident to CMSC 38000) Soare Math 30200 begins with models for defining computable functions such as the recursive functions and those computable by a Turing machine. Topics include the Kleene normal form theorem for representing computable functions and computably enumerable (c.e.) sets; the enumeration and s-m-n theorem, unsolvable problems, classification of c.e. sets, the Kleene arithmetic hierarchy, coding of information from one set to another, various degrees for measuring noncomputability, many-one, truth-table, and Turing degrees. The course also includes the Kleene recursion theorem and its applications, other fixed point theorems such as the Arslanov completeness criterion, elementary properties of Turing degrees, generic sets, and the construction of various non-c.e. degrees by oracle Kleene-Post constructions. Prereq: Math 25500 or consent of instructor. 30300. Computability Theory II (Ident to CMSC 38100)

38. Http://www.math.wisc.edu/graduate/guide-qe.htm Galois extensions and the fundamental theorem of Galois theory. . ultraproducts, saturated and special models, model completeness, Categoricity in power, http://www.math.wisc.edu/graduate/guide-qe.htm

Qualifying Exam Guide A Guide to Topics for the Qualifying Examinations This document describes the format and scope of Qualifying Exams in each of the six areas of graduate study. It is department policy that qualifiers be based on curriculum from the first year graduate sequences, as well as any undergraduate prerequisites, and that students who have mastered those courses should be able to pass the exams. Faculty members who set the exams are expected to implement this policy, and to adhere conscientiously to the guidelines that follow. Students, in turn, are expected to interpret each exam problem in a reasonable fashion, so as not to trivialize any solution. Copies of past exams and a record of previous passing scores are available from the department by request. Qualifying Exams typically take place the week or two before classes begin each semester (except summer); a precise schedule is posted months in advance. Faculty who grade the exams are expected to release the results before the last date for students to drop or withdraw from courses without receiving a DR or W on their transcripts, and within two weeks in any case. The books listed for each area below should be more than sufficient to cover topics that will appear on the exam. It should be emphasized, however, that the exams are intended to test general knowledge and competence rather than any particular set of books or courses. You can get previous years' exams in the

39. Dictionary Of The History Of Ideas this fact, since the axioms require neither Categoricity nor completeness because new games can always be invented and these can serve as prototypes for new http://etext.virginia.edu/cgi-local/DHI/dhi.cgi?id=dv2-32

40. Mathematics Course Descriptions Introductory logic and set theory, partitions and counting problems, elementary probability . independence, Categoricity, and completeness of the axioms. http://www.umsl.edu/bulletin/Home/College_of_Arts_and_Sciences/Mathematics_and_C

Courses in this section are grouped as follows: Mathematics, Computer Science, and Probability and Statistics. Students enrolling in introductory mathematics courses should check the prerequisites to determine if a satisfactory score on the Mathematics Placement Test is necessary. The dates on which this test is administered are given in the Schedule of Courses . Placement into introductory courses assumes a mastery of two years of high school algebra. A minimum grade of C- is required to meet the prerequisite requirement for any course except with permission of the department. The following courses fulfill the Natural Sciences and Mathematics [SM] breadth of study requirements: MATHEMATICS: 20, 30, 35, 50*, 70, 80, 100, 102, 105, 151*, 175, 180, 202, 203, 245, 255, 303, 304, 306, 310, 311, 316, 323, 324, 327, 335, 340, 341, 345, 350, 355, 358, 362, 364, 366, 367, 380, 389. COMPUTER SCIENCE: 22, 101, 122, 125, 170, 201, 224, 225, 240, 241, 255, 272, 273, 275, 278, 301, 302, 304, 305, 314, 325, 328, 330, 314, 344, 350, 352, 354, 356, 361, 362, 373, 374, 376, 377, 378, 379, 388, 389. PROBABILITY AND STATISTICS: 31, 132, 232, 320, 321, 326, 330, 331, 333, 339. Skip to Mathematics classes 100-level classes 200-level classes 300-level classes ... Skip to Probability and Statistics *Mathematics 50 and 151 fulfill this requirement only for students seeking the B.S. in education degree in Early Childhood Education, Elementary Education, and Special Education.

41. UCR CHASS: Department Of Philosophy Categoricity and completeness from Dedekind to Carnap and beyond, abstract The Development of Metamathematics and Proof Theory (with Jeremy Avigad), http://www.philosophy.ucr.edu/people/reck_e.html

Search: Home About Us Contact People ... Graduate Program Erich H. Reck Associate Professor of Philosophy Ph.D., University of Chicago, 1992 HMNSS 3206 erich.reck@ucr.edu Research Interests: Logic Philosophy of Mathematics Early Analytic Philosophy Sample Publications: Books and Collections: From Frege to Wittgenstein: Perspectives on Early Analytic Philosophy , E. Reck, ed., Oxford: Oxford University Press, 2002 Recent Articles: "Dedekind's Structuralism: An Interpretation and Partial Defense", Synthese , forthcoming Rudolf Carnap: From Jena to L.A. , Chicago: Open Court, forthcoming "Completeness and Categoricity, Part II: 20th Century Metalogic to 21st Century Semantics" (with Steve Awodey), History and Philosophy of Logic 23, No. 2, 2002, pp. 77-94

42. Research And Publications Computable Categoricity for trees of finite height (with S. Lempp, C. McCoy, analogue of the completeness Theorem, turn out to be independent of ZFC. http://qcpages.qc.cuny.edu/~rmiller/research.html

Research and Publications Prof. Russell Miller Research Interests I study computability theory, the branch of mathematical logic concerned with finite algorithms and the mathematical problems which such algorithms can or cannot solve. By relativizing, one forms a partial order of the degrees of difficulty (the Turing degrees ) of such problems. Computable model theory, my specialty, applies such techniques to general mathematical structures such as fields, trees, linear orders, groups and graphs. At present my investigations focus particularly on fields, and on the possibility of extending results from them to differential fields. Traditional computable model theory only considers countable structures, but I am currently examining different ways of extending the notions of computable model theory to certain uncountable structures, either by examining the structures locally rather than globally, or by extending the notion of computability to ordinal time to allow computation of functions with larger domains. Publications Journal of Symbolic Logic pdf download Abstract: Slaman and Wehner have constructed structures which distinguish the computable Turing degree from the noncomputable degrees, in the sense that the spectrum of each structure consists precisely of the noncomputable degrees. Downey has asked if this can be done for an ordinary type of structure such as a linear order. We show that there exists a linear order whose spectrum includes every noncomputable Delta^0_2 degree, but not

43. Universal Graphs With Forbidden Subgraphs And Algebraic Closure F. Theory of Computation F.1 COMPUTATION BY ABSTRACT DEVICES Categoricity, algebraic closure, existential completeness, forbidden subgraph, http://portal.acm.org/citation.cfm?id=314230&dl=GUIDE,GUIDE&coll=GUIDE&CFID=1515

44. Towards Completeness: Husserl On Theories Of Manifolds 1890–1901 Husserl’s notion of definiteness, ie, completeness is crucial to shows that Husserl meant by definiteness what is today called ‘Categoricity’. http://nsdl.org/resource/2200/20070529232734710T

Skip to Main Content Skip to Footer Links This resource was selected by the National Science Digital Library. Search for more NSDL resources Return to top of the page View this resource in its own window View more information about this resource This resource is found in the following collection(s). Click on the collection logo for more information. Close this window Collection Name: SpringerLink Online Journals Collection Description: Subject(s): Behavioral Science; Biomedical and Life Sciences; Chemistry and Materials Science; Chinese Library of Science; Computer Science; Earth and Environmental Science; Engineering; Social Sciences; Mathematics and Statistics; Medicine; Physics and Astronomy; Russian Library of Science Education (General) Technology Health Mathematics Science Anthropology Economics Geography Psychology Collection Information: Title SpringerLink Online Journals Subject Keyword(s) Behavioral Science; Biomedical and Life Sciences; Chemistry and Materials Science; Chinese Library of Science; Computer Science; Earth and Environmental Science; Engineering; Social Sciences; Mathematics and Statistics; Medicine; Physics and Astronomy; Russian Library of Science Education (General) Technology Health Mathematics Science Anthropology Economics Geography Psychology Description Resource Type Text Resource Format text/html;charset=UTF-8

45. Logic | School Of Computing And Mathematics set theory is developed in an informal axiomatic spirit, based on Gödel’s and issues such as completeness and Categoricity are surveyed informally. http://www.scam.keele.ac.uk/mat-30006

@import "/misc/drupal.css"; @import "/modules/img_assist/img_assist.css"; @import "/modules/saved_nice_menus/nice_menus.css"; @import "/themes/newscam/style.css"; @import "/modules/tables/tables.css"; Skip navigation School of Computing and Mathematics Faculty of Natural Sciences Navigation Contact Us People Computing Mathematics ... Home Logic Module Number MAT-30006 Private Study 120 Hours Co-requisites None Pre-requisites MAT-20009 Semester Spring Module Resource Page MAT-30006 Weeks Credits Example Classes 8 Hours Lectures 22 Hours Level Module Description The aim of the module is to introduce mathematical concepts for examining philosophical questions about the nature of mathematics as a whole. It attempts to present a sophisticated perspective on mathematics in a way that is accessible to undergraduates. The first half of the module concerns the subject-matter of mathematics. The thesis is developed that all mathematical objects can be understood as sets; set theory is developed in an informal axiomatic spirit, based on G¶del’s notion of transfinite iteration of the 'set of' operation. The second half examines mathematical reasoning, which is formalised as predicate calculus and studied metamathematically. The basic apparatus of formal semantics is introduced, and issues such as completeness and categoricity are surveyed informally.

46. Model Theory. Goedel's Completeness Theorem. Skolem's Paradox. Ramsey's Theorem. model theory, Skolem paradox, Ramsey theorem, Loewenheim, categorical, Ramsey, Skolem, Gödel, completeness theorem, Categoricity, Goedel, theorem, http://www.ltn.lv/~podnieks/gta.html

model theory, Skolem paradox, Ramsey theorem, Loewenheim, categorical, Ramsey, Skolem, Gödel, completeness theorem, categoricity, Goedel, theorem, completeness, Godel Back to title page Left Adjust your browser window Right Appendix 1. About Model Theory Some widespread Platonist superstitions were derived from other important results of mathematical logic (omitted in the main text of this book): Goedel's completeness theorem for predicate calculus, Loewenheim-Skolem theorem, the categoricity theorem of second order Peano axioms. In this short Appendix I will discuss these results and their methodological consequences (or lack of them). All these results have been obtained by means of the so-called model theory . This is a very specific approach to investigation of formal theories as mathematical objects. Model theory is using the full power of set theory. Its results and proofs can be formalized in the set theory ZFC Model theory is investigation of formal theories in the metatheory ZFC. The main structures of model theory are interpretations . Let L be the language of some (first order) formal theory containing constant letters c , ..., c

47. The Journal Of Symbolic Logic, Volume 41 626638 BibTeX Erik Ellentuck Categoricity Regained. 639-643 BibTeX Harrie C. M. de Swart Another Intuitionistic completeness Proof. http://www.informatik.uni-trier.de/~ley/db/journals/jsyml/jsyml41.html

The Journal of Symbolic Logic , Volume 41 Volume 41, Number 1, March 1976 Chi Tat Chong : An alpha-Finite Injury Method of the Unbounded Type. 1-17 BibTeX Michael Beeson : The Unprovability in Intuitionistic Formal Systems of the Continuity of Effective Operations on the Reals. 18-24 BibTeX Julia F. Knight : Omitting Types in Set Theory and Arithmetic. 25-32 BibTeX William Boos : Infinitary Compactness without Strong Inaccessibility. 33-38 BibTeX Charles E. Hughes : Two Variable Implicational Calculi of Prescribed Many-One Degrees of Unsolvability. 39-44 BibTeX Charles E. Hughes : A Reduction Class Containing Formulas with one Monadic Predicate and one Binary Function Symbol. 45-49 BibTeX Ronald Fagin : Probabilities on Finite Models. 50-58 BibTeX Victor Harnik : Approximation Theorems and Model Theoretic Forcing. 59-72 BibTeX Zofia Adamowicz : One More Aspect of Forcing and Omitting Types. 73-80 BibTeX Dov M. Gabbay : Completeness Properties of Heyting's Predicate Calculus with Respect to RE Models. 81-94 BibTeX Volker Weispfenning : Negative-Existentially Complete Structures and Definability in Free Extensions. 95-108 BibTeX Anders M. Nyberg

48. Peter Suber, "Logical Systems, Predicate Logic Review" how first order theories (FOTs) differ from QS; logical / proper axioms Categoricity of systems; Categoricity; why no consistent FOT is categorical http://www.earlham.edu/~peters/courses/logsys/revpl.htm

Logical Systems Predicate Logic Review Peter Suber Philosophy Department Earlham College Here I try to list all the important terms, distinctions, symbols, and results from the second half of the course, focusing on the metatheory of first order predicate logic. It wouldn't help much as a study guide if I listed everything we covered. You can get that by re-reading Hunter. I've tried to limit the list to what's most important. Believe it or not, I've omitted a lot. The topics are only roughly in the order in which we encountered them. I've adjusted this order when I thought it important to cluster related topics together. I've put in some blank lines to separate clusters from one another. I believe that all the technical terms on this list are defined in my glossary . If any are not, please let me know and I'll revise the glossary. For a review sheet from the first half of the course, focusing on infinite sets and truth-functional propositional logic, see the mid-term review predicate constants predicates / terms individual constants / individual variables universal quanitier / existential quantifier how to define the existential quantifier through the universal quantifier and negation (and vice versa why terms can contain terms why functions and their terms together are terms why predicates and their terms together are not terms quantifier scope bound / free variables why a variable can be both free and bound in the same wff closure of a wff open / closed wffs vacuous quantifiers one-place (monadic) predicates / many-place (polyadic) predicates

49. CARNEGIE MELLON UNIVERSITY PROGRAM IN PURE AND APPLIED LOGIC LOGIC I will emphasize aspects of the theory that may eventually converge to a proof cases of Shelah s Categoricity conjecture which is the prominent open problem http://logic.cmu.edu/pal-courses-f04.txt

CARNEGIE MELLON UNIVERSITY PROGRAM IN PURE AND APPLIED LOGIC LOGIC AND LOGIC-RELATED COURSES AND SEMINARS FOR FALL 2004 21-600 Mathematical Logic I Instructor: Peter Andrews MWF 11:30am-12:20pm Baker Hall A53 12 Units Description: The study of formal logical systems which model the reasoning of mathematics, scientific disciplines, and everyday discourse. Propositional calculus and first-order logic. Syntax, axiomatic treatment, derived rules of inference, proof techniques, computer-assisted formal proofs, normal forms, consistency, independence, semantics, soundness, completeness, the Lowenheim-Skolem Theorem, compactness, equality. 21-602 Set theory I INSTRUCTOR: Ernest Schimmerling TuTh 3:00-4:20 pm OSC 201 12 units DESCRIPTION: First semester graduate level set theory. The main topics are ZFC, infinitary combinatorics, relative consistency, constructibility, and descriptive set theory. TEXTBOOK: Kenneth Kunen, "Set Theory : An Introduction to Independence Proofs" COMMENT: Students should have a background in undergraduate level set theory (e.g., 21-229) and logic, which includes a working knowledge of basic ordinal and cardinal arithmetic, G¶del's completeness theorem, and the downward L¶wenheim-Skolem theorem. An understanding of the statement (but not the proof) of G¶del's theorem on consistency proofs will also be assumed. Those without the required background should meet with the instructor as soon as possible to discuss their options, which may include doing some reading over the summer. Set Theory I is a prerequisite for Set Theory II (21-702), which will be taught by Professor Uri Abraham in Spring, 2005. 80-310/610 Logic and Computation Instructor: Jeremy Avigad TuTh 3:00-4:20 pm Hamerschlag Hall B103 12 units Description: Among the most significant developments in logic in the twentieth century is the formal analysis of the notions of provability and semantic consequence. For first-order logic, the two are related by the soundness and completeness theorems: a sentence is provable if and only if it is true in every interpretation. This course begins with a formal description of first-order logic, and proofs of the soundness and completeness theorems. Other topics may include: compactness, the Lowenheim-Skolem theorems, nonstandard models of arithmetic, definability, other logics, and automated deduction. Prerequisites: 80-210, 80-211, or equivalent background in first-order logic. 80-315/615 Modal Logic Instructor: Horacio Arlo-Costa Wed 1:30-3:50 pm Baker Hall 150 9-12 units. Description: An introduction to first-order modal logic. The course considers several modalities aside from the so-called alethic ones (necessity, possibility). Epistemic, temporal or deontic modalities are studied, as well as computationally motivated modals (like "after the computation terminates"). Several conceptual problems in formal ontology that motivated the field are reviewed, as well as more recent applications in computer science and linguistics. Kripke models are used throughout the course, but we also study recent Kripkean-style systematizations of the modals without using possible worlds. Special attention is devoted to Scott-Montague models of the socalled "classical" modalities. Prerequisites: 80-210, or 80-211, or instructor's permission. 1-703 Model theory II INSTRUCTOR: Rami Grossberg MWF 10:30 Baker Hall 231A 12 units DESCRIPTION: This is a second course in model theory. The main topic of discussion will be classification theory for non-elemntary classes. TEXTBOOK: No official text. DETAILS: I will concentrate in what is the deepest part of pure model theory. Namely non-first order theories. In a typical case we will deal with abstract elementary classes. An AEC is essentially a class K of models all of the same similarity type (or a category of sets) which is closed under direct limits and little more. The aim is to have an analysis of such general classes. Most of the material to be discussed appears in (badly written) papers only. I will start with minimal prerequisites, but will progress quickly to some of the research frontieers of the field. I will emphasize aspects of the theory that may eventually converge to a proof cases of Shelah's categoricity conjecture which is the prominent open problem in the field, it is a parallel to Morley's theorem for L ?1,?, most results will be about more general classes. The common to all these classes is that the compactness theorem fails badly. Hopefully some of the techniques will turn to be usefull also in the study of classes of finite models, but we will concentrate at uncountable models. There will be a more serious use of set theory than needed for model theory of first-order logic. PREREQUISITES: About half of a basic graduate course in set theory and parts of an elementary model theory (about 60-70% of 21-603 ) or permission of the instructor. 80-411/711 Proof Theory Instructor: Jeremy Avigad TuTh 10:30-11:50 am Baker Hall 231A 12 units Description: This course is an introduction to Hilbert-style proof theory, where the goal is to represent mathematical arguments using formal deductive systems, and study those systems in syntactic, constructive, computational, or otherwise explicit terms. In the first part of the course, we will study various types of deductive systems (axiomatic systems, natural deduction, and sequent calculi) for classical, intuitionistic, and minimal logic. We will prove Gentzen's cut-elimination theorem, and use it to prove various theorems about first-order logic, including Herbrand's theorem, the interpolation theorem, the conservativity of Skolem axioms, and the existence and disjunction properties for intuitionistic logic. In the second part of the course, we will use these tools to study formal systems of arithmetic, including primitive recursive arithmetic, Peano arithmetic, and subsystems of second-order arithmetic. In particular, we will try to understand how mathematics can be formalized in these theories, and what types of information can be extracted using metamathematical techniques. A solid understanding of the syntax and semantics of first-order logic, as obtained from courses like 80-310/610 or 21-300/600, is required. A course covering issues topics like primitive recursion and coding, like 80-311/611 or 21-700, would be helpful, but is not essential. 15-814 Type Systems for Programming Languages INSTRUCTOR: Robert Harper TuTh 1:30-2:50pm Wean Hall 5409 12 units. DESCRIPTION: This course is an introduction to the theory and practice of type systems for programming languages. Topics include typed lambda calculus, subtyping, polymorphism, data abstraction, recursive types, and objects. PREREQUISITE: Background equivalent to programming skills and programming language exposure afforded by a typical undergraduate Computer Science degree. TEXTBOOK: Benjamin Pierce "Types and Programming Languages" MIT Press 2002. COMMENT: This course satisfies the CS distribution requirement in programming languages. Enrollment is limited to CS PhD students or permission of the instructor.

50. Course Descriptions - Mathematics Validity, provability, completeness, consistency, independence, Categoricity, decidability, Gödel s Theorem. Prerequisite(s) Mathematics 2000 http://www.uleth.ca/ross/courses/mathematics.html

// Put your additional javascripts in this slot site map contact us Registrar's Office and Student Services (ROSS) Programs ... Writing Centre Notice Board All the latest news and events. Go to Notice Board Web mail Access your email from anywhere. Go to Webmail Registrar's Office Timetables, calendars, and more... Go to Registrar's Office Email and Phone Listings Looking for someone? Find them here. See the Listings The Bridge Student and Employee Resources Go to The Bridge Library Today's Library Hours : Closed Go to the Library Web Tools Access on-line technology resources. Go to Web Tools //Start Tab Content script for UL with id="maintab" Separate multiple ids each with a comma. initializetabcontent("maintab") Course Descriptions - Mathematics University of Lethbridge Registrar's Office and Student Services (ROSS) > Course Descriptions - Mathematics Mathematics Essential Mathematics Credit hours: 3.0 Contact hours per week: 3-0-1 Polynomials and rational functions, trigonometry, exponential and logarithmic functions, inequalities, rudiments of probability and counting. This course may not be included among the mathematics courses required for Computer Science or Mathematics majors in Arts and Science.

51. Logic Colloquium 1997 - Contributed Papers Petr Hájek (Prague) Strong completeness of Gödel Logic (Proof Theory) . Andres Villaveces (Jerusalem) Categoricity Spectrum for Abstract Elementary http://www.amsta.leeds.ac.uk/events/logic97/con.html

LOGIC COLLOQUIUM 1997 Contributed Papers Papers accepted for presentation in person: Yoshihiro Abe (Yokohama): (Set Theory Section) Gabriel Aguilera, Inma P. de Guzman, Manuel Ojeda-Aciego (Malaga): 'DP-Distributions: A New Efficiency Strategy for the TAS Reduction Method' (Theoretical Computer Science) Kiwamu Aoyama and Kenji Fukuzaki (Kagoshima, Japan): 'Direct Proof of the Equivalence of the Induction Scheme and the Least Number Principle for Open Formulas' (Model Theory) M.M. Arslanov and I.Sh. Kalimullin (Kazan State University): 'Weak Presentation of Partial Orderings' (Computability Theory) Serikhzan A. Badaev (Almaty): 'Effectively Minimal Enumerations' (Computability Theory) Arnold Beckmann 'How to Separate Fragments of Bounded Arithmetic by Methods from Ordinal Analysis' (Proof Theory) Anatoly P. Beltiukov (University of Udmurtia, Russia): 'Hierarchy of Small Subrecursive Operator Classes Based on Bounded Recursion' (Computability Theory) Elias Tahhan Bittar (Clermont-Ferrand): 'Strong Normalization Proofs for Cut Elimination in Gentzen's Sequent Calculi' (Proof Theory) Aleksander Blaszczyk (Silesian University): 'Regular Subalgebras of Complete Boolean Algebras' Dumitru Busneag (Craiova): 'Valuations on Hilbert Algebras' Domenico Cantone and Pietro Ursino (University of Catania): 'A Unifying Approach to Computable Set Theory' (Theoretical Computer Science) Enrique Casanovas (Barcelona): 'A Test for Expandability' (Model Theory) F. Collot

52. Neil Tennant The method we use for proving completeness is that of Henkin. Important examples of firstorder theories will be given, in fully explicit logical form, http://people.cohums.ohio-state.edu/tennant9/650.html

NEIL TENNANT tennant.9@osu.edu If you email me, please use the header PHIL 650: YOURNAME. Professor Department of Philosophy Winter Term 2006 PHIL 650: Symbolic Logic Lecture/seminar University Hall , Room 353 Times tba Aims of this course This course aims to provide a comprehensive coverage of the syntax and semantics of first-order languages, and the positive results concerning them. First-order languages contain the expressions "for some x ", "for every x " and " x is identical to y ", in addition to the connectives "not", "and", "or" and "if ... then ..." of propositional logic (which will have been studied in PHIL 250: Introduction to Symbolic Logic Topics We address various philosophical problems concerning reference, definite descriptions, predication, identity and existence; and cover the rudiments of informal set theory that are needed for a rigorous discussion of syntactic and semantic matters. We give a precise compositional grammar for the generation of well-formed expressions (both terms and formulae) of first-order languages. We give the famous Tarskian definition of