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1. Infinitary Logic (Stanford Encyclopedia Of Philosophy)
Aczel, P., 1973, Infinitary logic and the Barwise Compactness Theorem , Proceedings of the 1971 Bertrand Russell Memorial logic Conference (Uldum,
http://plato.stanford.edu/entries/logic-infinitary/
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##### Infinitary Logic
First published Sun Jan 23, 2000; substantive revision Fri Mar 3, 2006 sets makes it no longer necessary to regard formulas as inscriptions, and suggests the possibility of fashioning "languages" some of whose formulas would be naturally identified as infinite sets . A "language" of this kind is called an infinitary language : in this article I discuss those infinitary languages which can be obtained in a straightforward manner from first-order languages by allowing conjunctions, disjunctions and, possibly, quantifier sequences, to be of infinite length. In the course of the discussion it will be seen that, while the expressive power of such languages far exceeds that of their finitary (first-order) counterparts, very few of them possess the "attractive" features (e.g., compactness and completeness) of the latter. Accordingly, the infinitary languages that do in fact possess these features merit special attention. compactness problem second-order nature and are

2. Infinitary Logic - Wikipedia, The Free Encyclopedia
An Infinitary logic is a logic that allows infinitely long statements and/or infinitely long proofs. Infinitary logics have different properties from those
http://en.wikipedia.org/wiki/Infinitary_logic
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##### Infinitary logic
Those unfamiliar with mathematical logic or the concept of ordinals are advised to consult those articles first.
An infinitary logic is a logic that allows infinitely long statements and/or infinitely long proofs . Infinitary logics have different properties from those of standard first-order logic . In particular, infinitary logics often fail to be compact or complete. Notions of compactness and completeness that are equivalent in finitary logic sometimes are not so in infinitary logic. So for infinitary logics the notions of strong compactness and strong completeness are defined. In this article we shall be concerned with Hilbert-type infinitary logics, as these have been extensively studied and constitute the most straightforward extensions of finitary logic. These are not, however, the only infinitary logics around. Considering whether a certain infinitary logic named -logic is complete promises to throw light on the continuum hypothesis
##### Contents

3. Infinitary Logic --Â Britannica Online Encyclopedia
There are also studies, such as secondorder logic and Infinitary logics, that develop the model theory of nonelementary logic. Second-order logic contains,
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##### infinitary logic
A selection of articles discussing this topic.
##### model theory
There are also studies, such as second-order logic and infinitary logics, that develop the model theory of nonelementary logic. Second-order logic contains, in addition to variables that range over individual objects, a second kind of variable ranging over sets of objects so that the model of a second-order sentence or theory also involves, beyond the basic domain, a larger set (called its... No results were returned. Please consider rephrasing your query. For additional help, please review Search Tips Search Britannica for infinitary logic About Us Legal Notices ... Test Prep Other Britannica sites: Australia France India Korea ... Encyclopedia

4. Infinitary Logic
Infinitary logic. Carol Karp Jon Barwise Game formula. Lecturer prof. Jouko VÃ¤Ã¤nÃ¤nen; Schedule Tuesdays and Thursdays at 1416 during fall term 2003.
http://www.math.helsinki.fi/logic/opetus/inflog/
##### Infinitary logic
• Lecturer: prof.
• Schedule: Tuesdays and Thursdays at 14-16 during fall term 2003. First lecture on Sept 11th, 2003.
• Location: SIII
• Exercise classes: Tuesdays at 12-14, in room 420, Vuorikatu 20, 4th floor.
• Course material is in a folder on the fifth floor, and on WebCT pages.
• The course will concentrate on infinitary languages and back-and-forth systems.
• Participants will be given projects that can serve as a basis for master's thesis, licentiate thesis or doctoral thesis.
• The course will utilize the WebCT course management system.
• Prerequisites: Mathematical logic (57067-7). Basic set theory such as finite and infinite sets, denumerable sets, well-ordered sets, ordinals.
• 5. IngentaConnect Computing With Infinitary Logic
Infinitary logic (with finitely many variables) is a very powerful extension of these languages which provides an elegant unifying formalism for a wide
http://www.ingentaconnect.com/content/els/03043975/1995/00000149/00000001/art000
var tcdacmd="dt";

 6. CAT.INIST We prove that the Lindenbaum algebra generated by the Infinitary logic is a completely distributive lattice dual to the same SFPdomain.http://cat.inist.fr/?aModele=afficheN&cpsidt=1268948

 7. Infinitary Logic And Inductive Definability Over Finite Structures Infinitary logic and inductive definability over finite structures. Source, Information and Computation archive Volume 119 , Issue 2 (June 1995) table ofhttp://portal.acm.org/citation.cfm?id=203545

8. Barwise Infinitary Logic And Admissible Sets
Barwise Infinitary logic and admissible sets. H. Jerome Keisler and Julia F. Knight. Source Bull. Symbolic logic Volume 10, Issue 1 (2004), 436.
http://projecteuclid.org/handle/euclid.bsl/1080330272
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##### Bulletin of Symbolic Logic

9. Infinitary Logic And Inductive Definability Over Finite Structures
These languages can also be seen as fragments of an Infinitary logic where each formula has a bounded number of variables, L (see, for instance,
http://repository.upenn.edu/cis_reports/365/
 HOME SEAS CIS what's this? Technical Reports (CIS) Browse this Collection CIS Collections Search CIS Website ... Submit a Paper TITLE: Infinitary Logic and Inductive Definability over Finite Structures AUTHOR(S): Anuj Dawar, University of Pennsylvania Steven Lindell, University of Pennsylvania ... University of Pennsylvania DOCUMENT TYPE: Technical Report Download the Document (PDF format - 2.0 MB) - 27 November 1991 Tell a colleague about it. University of Pennsylvania Department of Computer and Information Science Technical Report No. MS-CIS-91-97. ABSTRACT: The extensions of first-order logic with a least fixed point operators (FO + LFP) and with a partial fixed point operator (FO + PFP) are known to capture the complexity classes P and PSPACE respectively in the presence of an ordering relation over finite structures. Recently, Abiteboul and Vianu [AV91b] investigated the relation of these two logics in the absence of an ordering, using a mchine model of generic computation. In particular, they showed that the two languages have equivalent expressive power if and only if P = PSPACE. These languages can also be seen as fragments of an infinitary logic where each formula has a bounded number of variables, L (see, for instance, [KV90]). We present a treatment of the results in [AV91b] from this point of view. In particular, we show that we can write a formula of FO + LFP and P from ordered structures to classes of structures where every element is definable. We also settle a conjecture mentioned in [AV91b] by showing that FO + LFP in properly contained in the polynomial time computable fragment of

 10. JSTOR Applications Of Strict \$\Pi^1_1\$ Predicates To Infinitary 336 R~vmws This paper is an important contribution to the related fields of Infinitary logic and generalisa tions of recursion theory; it is a sequel tohttp://links.jstor.org/sici?sici=0022-4812(197406)39:2<335:AOSPTI>2.0.CO;2-X

11. [math/9706225] Stationary Sets And Infinitary Logic
Stationary sets and Infinitary logic. Authors Saharon Shelah, Jouko VÃ¤Ã¤nÃ¤nen Reportno Shelah ShVa657 Subj-class logic
http://arxiv.org/abs/math/9706225
##### arXiv.orgmath
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##### Title: Stationary sets and infinitary logic
Authors: Saharon Shelah (Submitted on 15 Jun 1997) Abstract: Subjects: Logic (math.LO) Report number: Shelah [ShVa:657] Cite as: arXiv:math/9706225v1 [math.LO]
##### Submission history
From: Shelah Office [ view email
Sun, 15 Jun 1997 00:00:00 GMT (10kb)
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12. The Homepage Of The Helsinki Logic Group
Saharon Shelah and Jouko VÃ¤Ã¤nÃ¤nen, Stationary sets and Infinitary logic, Journal of Symbolic logic, 6513111320, 2000. Stevo Todorcevic and Jouko VÃ¤Ã¤nÃ¤nen,
http://www.logic.math.helsinki.fi/
##### The Helsinki Logic Group
University of Helsinki
Logiikan opetus

Logic Colloquium 2003: Group photo and lecture materials Members Research Publications ... Contact Info
##### Members
Members - Research Publications Links Contact Info ... Aapo Halko , Ph.D., descriptive set theory Alex Hellsten , Ph.D., set theory Taneli Huuskonen , docent, model theory, set theory, logic and analysis Tapani Hyttinen , docent, stability theory, infinitary logic Juliette Kennedy , docent, models of arithmetic, philosophy of mathematics Meeri KesÃ¤lÃ¤ , Ph.D., model theory Juha Kontinen , Ph.D., finite model theory Kerkko Luosto , docent, finite and infinite model theory, abstract model theory Juha Oikkonen , university lecturer, infinitary logic, nonstandard analysis Matti Pauna , Ph.D. Juha Ruokolainen , Ph.D. , professor, finite model theory, abstract model theory, set theory
##### Ph.D. students:
Tapio Eerola , M.Sc. , Ph.L. Jarmo Kontinen , M.Sc. Hannu NiemistÃ¶ , Ph.L., finite model theory Ville Nurmi , M.Sc. Ryan Siders , M.Sc. Former members of the group can be found in the list of Ph.Ds

13. Infinitary Logic - Article In The Stanford Encyclopaedia Of Philosophy By John L
Infinitary logic is a branch of formal logic where finitary formulae are replaced by potentially Infinitary mathematical entities.
http://www.sciencecentral.com/site/495638
 Sunday, 23 December, 2007 Home Submit Science Site Add to Favorite Contact search for Directories Aeronautics and Aerospace Agriculture Anomalies and Alternative Science Astronomy ... Technology Category: Science Math Logic and Foundations Nonstandard Logics and Extensions ... REPORT BROKEN LINK Infinitary Logic Popularity: Details document.write(''); Article in the Stanford Encyclopaedia of Philosophy by John L. Bell. Infinitary Logic is a branch of formal logic where finitary formulae are replaced by potentially infinitary mathematical entities. URL Title Infinitary Logic Description Category: Related sites Non Standard Logics (Popularity: ): A comprehensive listing of flavours of non-standard logic with brief descriptions and references, compiled by ... Logic System Interrelationships (Popularity: ): Shows how a number of representative logics fit together. The interrelationships usually given as something ... What are Weak Arithmetics (Popularity: ): Notes defining the subject. Available in HTML and PS formats. Computability Logic (Popularity: ): Wikipedia (free encyclopedia) article.

14. Infinitary Logic
Article in the Stanford Encyclopaedia of Philosophy by John L. Bell. Infinitary logic is a branch of formal logic where finitary formulae are replaced by
http://www.spacetransportation.org/Detailed/71159.html
##### Infinitary Logic
Infinitary Logic

Article in the Stanford Encyclopaedia of Philosophy by John L. Bell. Infinitary Logic is a branch of formal logic where finitary formulae are replaced by potentially infinitary mathematical entities.
http://plato.stanford.edu/entries/logic-infinitary/
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15. Cover Pages: ISO Common Logic Standard Proposed For Use With RDF, UML, DAML, And
Part 1 (FirstOrder logic) specifies the syntax and semantics of a language equivalent to first-order logic. Part 2 (Infinitary logic) is an expansion of
http://xml.coverpages.org/ni2002-04-08-a.html
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Created: April 08, 2002. News: Cover Stories
ISO Common Logic Standard Proposed for Use With RDF, UML, DAML, and Topic Maps. A posting from John Sowa without specifying which of the three concrete syntaxes was the original source or the intended target of the information." The development team "hopes that the CL standard can be used for many other languages that have a declarative semantics, such as RDF, UML, DAML, or Topic Maps. There will be an XML representation of the abstract categories, which will conform to all accepted W3C standards. There may also be XML representations of the concrete syntaxes as well; TPC notation will require Unicode for the special logical symbols, but they could also be represented, as in HTML and XML, by symbols like or
##### Principal references:
• "Common Logic Standard." Posting from John F. Sowa 2002-04-06. [ source Common Logic Standard website . Note the name change: 'Foundations for Logical Languages' is now 'Common Logic Standard'. Common Logic Standardization Meeting: Minutes . Stanford University. March 21-22, 2002. Mike Genesereth hosted a meeting of the working group on "proposed ISO standards for the Knowledge Interchange Format (KIF) and Conceptual Graphs (CGs)." Attendees: The meeting was attended, in whole or in part, by Michael Genesereth (host), Michael Gruninger (editor), Pat Hayes, John McCarthy, Chris Menzel, Adam Pease, John Sowa, Mark Stickel, and Charles White. [

16. Publications, H. Jerome Keisler
A Local Normal Form Theorem for Infinitary logic with Unary Quantifiers (with W. Lotfallah). Mathematical logic Quarterly 51 (2005), pp. 137144.
http://www.math.wisc.edu/~keisler/papers.html
##### Publications, H. Jerome Keisler
1. Theory of models with generalized atomic formulas, J. Symbolic Logic 25 (1960), pp. 1-26. 2. Ultraproducts and elementary classes, Ph. D. Thesis, Univ. of California, Berkeley, 1961, 45 pages. 3. On some results of Jonsson and Tarski concerning free algebras, Math. Scand. 9 (1961), pp. 102-106. 4. Ultraproducts and elementary classes, Indag. Math. 23 (1961), pp. 477-495. 5. Some applications of the theory of models to set theory, Proc. Int. Cong. of Logic, Methodology, and Philosophy of Science, Stanford 1962, pp. 80-85. 6. Model theories with truth values in a uniform space (with C.C.Chang), Bull. Amer. Math. Soc. 68 (1962), pp. 107-109. 7. An improved prenex normal form (with C.C.Chang), J. Symbolic Logic 27 (1962), pp. 317-326. 8. Applications of ultraproducts of pairs of cardinals to the theory of models (with C.C.Chang), Pacific J. Math. 12 (1962), pp. 835-845. 9. Limit ultrapowers, Trans. Amer. Math. Soc. 107 (1963), pp. 382-408. 10. A complete first-order logic with infinitary predicates, Fund. Math. 52 (1963), pp. 177-203. 11. Good ideals in fields of sets, Annals of Math. 79 (1964), pp. 338-359.

17. Infinitary Logic - Spock Search
Anonymous Spocker, Anonymous Spocker, Anonymous Spocker and other people matching \
http://www.spock.com/q/Infinitary-logic
 Processing (could take a few minutes)... You should enable javascript to use Spock Name or Email: Tags: Example: baptist democrat Location: Example: San Francisco, CA Age: any to any male female any Must have picture! Click here to see where people you know are on the web Login Sign up Grid ... Carol Karp female University of Maryland Michigan State University mathematician breast cancer ... Add tag Carol Karp nÂ©e Carol Ruth Vander Velde American mathematician of Dutch ancestry. Best known for her work on infinitary logic, she also played v... See: Tags (9) Pictures (0) Related People (0) News Web: Wikipedia Jon Barwise male, deceased ErdÃÂs number 2 Stanford University proposition Liar paradox ... Add tag Kenneth Jon Barwise (June 29, 1942 - March 5, 2000) was a U.S. mathematician, philosopher and logician who proposed some fundamental revisions to... See: Tags (24) Pictures (5) Related People (0) News Web: Wikipedia math.ucla.edu

18. ICDT 1992: 113-123
Infinitary logic in FiniteModel Theory. LICS 1992 46-57 BibTeX; SF88 U88 Jeffrey D. Ullman Principles of Database and Knowledge-Base Systems,
http://www.informatik.uni-trier.de/~ley/db/conf/icdt/AbiteboulVV92.html
##### Computing with Infinitary Logic.
Serge Abiteboul Moshe Y. Vardi Victor Vianu : Computing with Infinitary Logic. ICDT 1992 DBLP BibTeX
##### ACM SIGMOD Anthology
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##### Journal Version
Serge Abiteboul Moshe Y. Vardi Victor Vianu : Computing with Infinitary Logic. Theor. Comput. Sci. 149(1) BibTeX
##### References
Foto N. Afrati Stavros S. Cosmadakis Mihalis Yannakakis : On Datalog vs. Polynomial Time. PODS 1991 BibTeX
Serge Abiteboul Victor Vianu : Datalog Extensions for Database Queries and Updates. J. Comput. Syst. Sci. 43(1) BibTeX
Serge Abiteboul Victor Vianu : Generic Computation and Its Complexity. STOC 1991 BibTeX
Serge Abiteboul Victor Vianu : Computing with First-Order Logic.

19. [FOM] Infinitary Logic And `core Mathematics'
I have just posted the article The complex numbers and \\ complex exponentiation\\ Why Infinitary logic is necessary! at
http://cs.nyu.edu/pipermail/fom/2006-April/010370.html
##### [FOM] infinitary logic and `core mathematics'
John Baldwin jbaldwin at uic.edu
Sun Apr 9 19:05:26 EDT 2006

20. Infinitary Logic (Stanford Encyclopedia Of Philosophy/Summer 2004 Edition)
Infinitary logic. Traditionally, expressions in formal systems have been regarded as signifying finite inscriptions which areÂat least in principleÂcapable
http://www.science.uva.nl/~seop/archives/sum2004/entries/logic-infinitary/
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##### Infinitary Logic
sets makes it no longer necessary to regard formulas as inscriptions, and suggests the possibility of fashioning "languages" some of whose formulas would be naturally identified as infinite sets . A "language" of this kind is called an infinitary language : in this article I discuss those infinitary languages which can be obtained in a straightforward manner from first-order languages by allowing conjunctions, disjunctions and, possibly, quantifier sequences, to be of infinite length. In the course of the discussion it will be seen that, while the expressive power of such languages far exceeds that of their finitary (first-order) counterparts, very few of them possess the "attractive" features (e.g., compactness and completeness) of the latter. Accordingly, the infinitary languages that do in fact possess these features merit special attention. compactness problem second-order nature and are

21. Prof. David Harel - Books
3.1 What is logic? 3.2 Propositional logic 3.3 Equational logic 3.4 Predicate logic 3.5 EhrenfeuchtFraisse Games 3.6 Infinitary logic 3.7 Modal logic
http://www.wisdom.weizmann.ac.il/~dharel/dynamic_logic.html
Preface
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##### Part I: Fundamental Concepts
1. Mathematical Preliminaries
1.1 Notational Conventions
1.2 Sets
1.3 Relations
1.4 Graphs and Dags
1.5 Lattices
1.6 Transfinite Ordinals
1.7 Set Operators
1.8 Bibliographical Notes 1.9 Exercises 2. Computability and Complexity 2.1 Machine Models 2.2 Complexity Classes 2.3 Reducibility and Completeness 2.4 Bibliographical Notes 2.5 Exercises 3. Logic 3.1 What is Logic? 3.2 Propositional Logic 3.3 Equational Logic 3.4 Predicate Logic 3.5 Ehrenfeucht-Fraisse Games 3.6 Infinitary Logic 3.7 Modal Logic 3.8 Bibliographical Notes 3.9 Exercises 4. Reasoning About Programs 4.1 States and Executions 4.2 Programs 4.3 Program Verification

22. CSLI Calendar, 8 December 1994, Vol.10:10
logic LUNCH on Friday, 9 December 1200 noon, Building 380, Room 383N Fixpoint logic versus Infinitary logic in Finite Model Theory Phokion G.
http://www-csli.stanford.edu/Archive/calendar/1994-95/msg00009.html
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• To : friends Subject : CSLI Calendar, 8 December 1994, vol.10:10 From Date : Wed, 7 Dec 1994 11:27:32 -0800
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24. Infinitary Logic - Mathematics Dictionary And Research Guide
Infinitary logic Those unfamiliar with mathematical logic or the concept of ordinals are advised to consult those articles firs.
http://www.123exp-math.com/t/0170949056/
The Language of Mathematics - Dictionary and Research Guide Provided by
##### Infinitary logic
Those unfamiliar with mathematical logic or the concept of ordinals are advised to consult those articles first.
##### Keywords and Synonyms
• Infinitary logic, Infinite logic, Infinitary logics, Infinitary language

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Last update: December 19, 2007

25. Infinitary Logic (Stanford Encyclopedia Of Philosophy/Spring 2007 Edition)
Infinitary logic. First published Sun Jan 23, 2000; substantive revision Fri Mar 3, 2006. Traditionally, expressions in formal systems have been regarded as
http://www.seop.leeds.ac.uk/archives/spr2007/entries/logic-infinitary/
Spring 2007 Edition Cite this entry Search this Archive Advanced Search Table of Contents ... Stanford University This is a file in the archives of the Stanford Encyclopedia of Philosophy
##### Infinitary Logic
First published Sun Jan 23, 2000; substantive revision Fri Mar 3, 2006 sets makes it no longer necessary to regard formulas as inscriptions, and suggests the possibility of fashioning "languages" some of whose formulas would be naturally identified as infinite sets . A "language" of this kind is called an infinitary language : in this article I discuss those infinitary languages which can be obtained in a straightforward manner from first-order languages by allowing conjunctions, disjunctions and, possibly, quantifier sequences, to be of infinite length. In the course of the discussion it will be seen that, while the expressive power of such languages far exceeds that of their finitary (first-order) counterparts, very few of them possess the "attractive" features (e.g., compactness and completeness) of the latter. Accordingly, the infinitary languages that do in fact possess these features merit special attention. compactness problem second-order nature and are

26. A Note On Extensions Of Infinitary Logic
A Note on Extensions of Infinitary logic. Authors, Shelah, Saharon; VÃ¤Ã¤nÃ¤nen, Jouko. Publication, eprint arXivmath/0009080. Publication Date, 09/2000
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 27. Toward An Infinitary Logic Of Domains: Abramsky Logic For Transition Systems Home Journals and Conference Proceedings Information and Computation. Toward an Infinitary logic of Domains Abramsky logic for Transition Systemshttp://wotan.liu.edu/docis/show?doc=dbl/infcom/1999_155_1_2_170_TAILOD.htm&query

28. Model Theory For Infinitary Logic: Logic With Countable Conjunctions And Finite
Model Theory for Infinitary logic logic with Countable Conjunctions and Finite Quantifiers; KEISLER, H. JEROME,. Offered by Black Oak Books, Berkeley.
http://www.antiqbook.com/boox/blac/589061.shtml
 ANTI Q BOOK Search Antiqbook Ask a question or Order this book Browse our books ... Book dealer info KEISLER, H. JEROME, Model Theory for Infinitary Logic: Logic with Countable Conjunctions and Finite Quantifiers Amsterdam North-Holland Publishing Company, 1971. Hardcover, Cloth, Good. out of print. Small red stain on back cover. Clean interior. Tight binding. US\$ 85.00 Offered by: Black Oak Books, Berkeley - Book number: 589061 See more books from our catalog: Mathematics Hundreds of the world's finest antiquarian and used booksellers offer their books on Antiqbook. They offer full satisfaction and normal prices - no markups, no hidden costs, no overcharged shipping costs. 7 million books at your fingertips! Search all books at Antiqbook

 29. MnoGoSearch: Infinitary definability in boundedvariable Infinitary logic; the logical analogues of . are not fragments of bounded-variable Infinitary logic IA Stewart 1996/11http://www.mcs.le.ac.uk/cgi-bin/search.cgi?q=infinitary

30. Front: [math.LO/0009080] A Note On Extensions Of Infinitary Logic
Title A Note on Extensions of Infinitary logic Authors Saharon Shelah, Jouko VÃ¤Ã¤nÃ¤nen Categories math.LO logic Report number Shelah ShVa726
http://front.math.ucdavis.edu/math.LO/0009080
 Front for the arXiv Mon, 24 Dec 2007 Front math LO math.LO/0009080 search register submit journals ... iFAQ math.LO/0009080 Title: A Note on Extensions of Infinitary Logic Authors: Saharon Shelah , Jouko VÂ¤Â¤nÂ¤nen Categories: math.LO Logic Report number: Shelah [ShVa:726] Abstract: Owner: Saharon Shelah's Office Version 1: Thu, 7 Sep 2000 20:18:27 GMT - for questions or comments about the Front arXiv contact page - for questions about downloading and submitting e-prints

31. Scientific Commons Hierarchies In Transitive Closure Logic
We establish a general hierarchy theorem for quantifier classes in the Infinitary logic L ! 1! on finite structures. In particular, it is shown that no
http://en.scientificcommons.org/400317

32. Computational Model Theory: An Overview -- Vardi 6 (4): 601 -- Logic Journal Of
These observations motivated the introduction of two abstract formalisms that of finitevariable Infinitary logic and that of relational machines.
http://jigpal.oxfordjournals.org/cgi/content/abstract/6/4/601
@import "/resource/css/hw.css"; @import "/resource/css/igpl.css"; Skip Navigation Oxford Journals Logic Journal of IGPL 1998 6(4):601-624; doi:10.1093/jigpal/6.4.601
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##### Computational model theory: an overview
MY Vardi Department of Computer Science, Rice University, Houston, TX 77005-1892, USA e-mail: vardi@cs.rice.edu, URL: http://www.cs.rice.edu/ vardi The computational complexity of a problem is the amount of resources, such as time or space, required by a machine that solves the problem. The descriptive complexity of problems is the complexity of describing problems in some logical formalism over finite structures. One of the exciting developments in complexity theory

33. Carol Karp
LopezEscobar, E. G. K. Introduction, Infinitary logic In Memoriam Carol Karp, Lecture Notes in Mathematics, Vol. 492, Springer-Verlag 1975.
http://www.agnesscott.edu/Lriddle/women/karp.htm
##### Biographies of W omen Mathematicians
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##### Carol Karp
August 10, 1926 - August 20, 1972 Carol Ruth Vander Velde was born in Forest Grove, Michigan, part of the Dutch farming community near Holland, Michigan. She attended school there and in Ohio where her family moved when she was 11. She graduated with distinction from Manchester College, Indiana, in 1948, and then earned a master's degree in mathematics from Michigan State University in 1950. Before entering the graduate program in mathematics at the University of Southern California in 1951, she spent time as a violist in a touring all-woman orchestra. During her first year at USC, Carol married Arthur Karp. During the next 8 years she pursued her graduate studies while following her thesis advisor, Leon Henkin, and her husband around the country and the world. She spent two years at the University of California at Berkeley and parts of the years 1957 and 1958 in Japan where her husband was stationed in the Navy. In 1958 she accepted a position at the University of Maryland. Karp finally received her Ph.D. from the University of Southern California in 1959 with a dissertation on "Languages with expressions of infinite length" [ Abstract Karp spent her entire career at the University of Maryland, reaching the rank of professor only 7 years after earning her Ph.D. She was a highly respected member of the international logic community and a leader in the developing theory of infinitary logic. Her book

34. The Infinitary Logic Of Sparse Random Graphs
Let L be the Infinitary language obtained from the firstorder language of graphs by closure under conjunctions and disjunctions of arbitrary sets of
http://csdl.computer.org/comp/proceedings/lics/1995/7050/00/70500046abs.htm

 35. ODOBS - Publication Page: Computing With Infinitary Logic. (1982); Anuj DAWAR, Steven LINDELL, Scott WEINSTEIN Infinitary logic and Inductive Definability over Finite Structures (1995); Phokion G.http://lupus.cs.uni-dortmund.de:8080/odobs/publication;jsessionid=28DE89002C68D5

36. Lumpy Pea Coat: Simulated Class Quantification
If we want to do set theory and not be committed to sets, then maybe an Infinitary logic that allows simultaneous quantification over infinitely many
http://nortexoid.blogspot.com/2006/08/simulated-class-quantification.html
##### Lumpy Pea Coat
Logic and Mannequins
##### Simulated class quantification
Quine endorses what he calls "simulated" class quantification in Philosophy of Logic (pp. 72-74). The idea is this. Suppose the object language to have only finitely many atomic predicates P1,...,Pn. For any formula in which a predicate, say Pi, occurs (which we will write as '...Pi...'), we can simulate existential quantification over Pi in '...Pi...' (which we will write as (EPi)(...Pi...)) by the disjunction ...P1... or ...P2... or...or ...Pn...
Obviously this works only on account that there are finitely many atomic predicates. And if you think about it, it lets you simulate quantification over only a very restricted set of "classes", viz. the Pi. It is common practice, however, to think of each open formula with n free variables as an n-ary predicate. But since there are infinitely many n-ary predicates in this sense (i.e. there are infinitely many open formulas with n free variables), it will be impossible to simulate quantification over them (unless conjunction/disjunction over infinitely many formulas is allowedbut in the context of PoL, i.e. classical logic, it is not).
In fact, simulated quantification seems so useless that one has to wonder why he dedicated an entire section of PoL to it.

37. New Set Theory
We introduce almost selfreferential formulas, use them to extend set theory, and relate their expressive power to that of Infinitary logic.
http://web.mit.edu/dmytro/www/NewSetTheory.htm
Dmytro Taranovsky April 20, 2005
##### Extending the Language of Set Theory
Abstract: We discuss the problems of incompleteness and inexpressibility. We introduce almost self-referential formulas, use them to extend set theory, and relate their expressive power to that of infinitary logic. We discuss the nature of proper classes. Finally, we introduce and axiomatize a powerful extension to set theory. List of Sections: Introduction and Outline Incompleteness and Inexpressibility Almost Self-Referential Formulas Expressive Power of the Extensions ... Higher Order Set Theory
##### Introduction and Outline
Despite vast advances in set theory and mathematics in general, the language of set theory, which is also the language of mathematics, has remained the same since the beginning of modern set theory and first order logic. That formal language has served us well, but it is of necessity limited, and does not adequately deal with properties for which there is no set of all objects satisfying the property. The purpose of this paper is to address the deficiencies in the expressive power of ordinary set theory. The second section discusses incompleteness and inexpressibility in general. Much of the paper discusses logic that allows some self-reference but with limitations to prevent loops and infinite regress. The logic is more expressive than (a formulation of) infinitary logic. We show that levels of infinitary logic correspond to levels of almost self-referential logic and levels of constructible hierarchy above V. We use strong logics and weak set theories to clarify the strengths of inaccessible and Mahlo cardinals. We also use large cardinals to get reflection principles, and use reflection principles to axiomatize extensions to the language of set theory.

38. ICALP'07: Accepted Papers - Track B
In particular, we show that if this variety admits either the unary or affine type, the corresponding CSP is not definable in the Infinitary logic with
http://icalp07.ii.uni.wroc.pl/acceptl-trackb.html
ICALP 2007 34th International Colloquium on
Automata, Languages and Programming Colocated with LICS 2007, LC 2007, and PPDP 2007 Overview Call for Papers Program Committee ... Submissions (closed) Accepted papers short list, alphabetic list with abstracts Online proceedings (NEW!) ... Other events in July in WrocÃÂaw
##### List of accepted papers
(In order of appearance)
##### Track B: Logic, Semantics and Theory of Programming
Modular Algorithms for Heterogeneous Modal Logics Lutz SchrÂ¶der and Dirk Pattinson
State-based systems and modal logics for reasoning about them often heterogeneously combine a number of features such as non-determinism and probabilities. Here, we show that the combination of features can be reflected algorithmically and develop modular decision procedures for heterogeneous modal logics. The modularity is achieved by formalising the underlying state-based systems as multi-sorted coalgebras and associating both a logical and an algorithmic description to a number of basic building blocks. Our main result is that logics arising as combinations of these building blocks can be decided in polynomial space provided that this is the case for the components. By instantiating the general framework to concrete cases, we obtain PSPACE decision procedures for a wide variety of structurally different logics, describing e.g. Segala systems and games with uncertain information.

39. Philosophy: Reference: Stanford-encyclopedia-of-philosophy: Page 5
Infinitary logic is a branch of formal logic where finitary formulae are replaced by potentially Infinitary mathematical entities. By John L. Bell.
http://www.spiritandsky.com/philosophy/reference/stanford-encyclopedia-of-philos

Home
Search Suggest a Site Submission Guidelines ... Linking
##### philosophy: reference: stanford-encyclopedia-of-philosophy: Page 5
Below is a listing of categories in the SKR pertaining to philosophy: reference: stanford-encyclopedia-of-philosophy: Page 5
##### Homephilosophyreferencestanford-encyclopedia-of-philosophy : Page 5
• Fuzzy Logic Fuzzy Logic Survey of logical systems with a continuum of truth values; by Petr HÃÂ«ÃÂ¡jek.
(Added: Thu Jan 01 2004) ID 116700
• Game Theory Game Theory Von Neumann and Morgensterns mathematical theory of bargaining, introduced by Don Ross University of Cape Town.
(Added: Thu Jan 01 2004) ID 116443
• George Santayana George Santayana Life and effort of early 20th century Spanish-born American philosopher; by Herman Saatkamp.
(Added: Thu Jan 01 2004) ID 116624
• Giambattista Vico Giambattista Vico Life and effort of 18th century Italian philosopher; by Timothy Costelloe.
(Added: Thu Jan 01 2004) ID 116713
• Globalization Globalization Social theory and philosophy issues in globalization; by William Scheuerman. (Added: Thu Jan 01 2004) ID 116577
• Gottlob Frege Gottlob Frege Edward N. Zalta of the Metaphysics Research Lab.

 40. Books, Surveys @BOOK{EFfinmt, AUTHOR = Heinz-Dieter Ebbinghaus Infinitary logic in FiniteModel Theory , BOOKTITLE = Proceedings 7th Annual IEEE Symp.\ on logic in Computer Science, LICS 92, Santa Cruz, CA, USA,http://www.cs.ioc.ee/~tarmo/bibs/fmt.bib

 41. CWI Report(s) Of: Software Engineering (SEN)(1999) Towards an Infinitary logic of domains Abramsky logic for transition systems M.M. Bonsangue; J.N. Kok; 1999, SENR9924, ISSN 1386-369Xhttp://db.cwi.nl/rapporten/index.php?jaar=1999&dept=15

42. McColm's Research
Hierarchies in Transitive Closure logic, Stratified Datalog, and Infinitary logic, (with E. Graedel, at the Lehrgebiet Mathematische Grundlagen der
http://www.math.usf.edu/~mccolm/Research.html
##### Mathematical Research
Currently, I am trying to understand mathematical games and random structures. I have some pages for logical and combinatorial games linked from this page, and I will be putting up some stuff on random structures in the foreseeable future. The most of this page is devoted to past papers. I am trying to understand mathematical games - i.e., those things known as "mathematical games" by logicians and combinatorists, and as "extended games" by game theorists. So what I am doing in this web-site is describing some important research (including my own) with references for people who want to explore further. Since I am trying to learn something about these subjects, I appreciate questions, comments, and even (gentle) criticism. I especially appreciate new kinds of games and new models of random structures, and other areas of game theory that I have missed. Perhaps I should explain where I am coming from. I got a Ph.D. in mathematics from UCLA in 1986, where I had worked on abstract recursion under Yiannis Moschovakis. (The kind of abstract recursion I worked on was elementary induction, which is now called Least Fixed Point logic, or just LFP to very theoretical computer scientists.) Most of my thesis was on recursion on infinite models, but I soon was doing work on finite models. I also spent some time working on ramsey theory, and also in analysis. More recently, I became convinced that pebble games were the key to understanding LFP. I do not mean the pebble games developed by Ehrenfeucht, I mean the more ancient game of the sort: you have a statement P and a structure M, and there are two players, call them Eloise and Abelard (some people call them I and II, or Angel and Demon, or Assertor and Denier). They play a game on M in such a way that Eloise has a winning strategy iff P is true on M. For example, if M was a graph, and P was the statement "the graph is connected", then the game would be as follows.

43. 1992-93 Stanford Theory Colloquium Calendar
Infinitary logic extends firstorder logic by allowing Infinitary conjunctions and One usually think of Infinitary logic as a fairly esoteric logic,
http://theory.stanford.edu/~aflb/colloq-archive.html
STC is the Stanford Theory Colloquium. What follows is an archive of many of the talks that have been given in the Colloquium. Talks are often held in Jordan Hall, on the Main Quad of Stanford's Campus. Click here for directions. Talks are also held in the Gates Building, near the Main Quad of Stanford's campus. Click here for directions.
##### Contents:
• 16 April 1997 Bernard Chazelle (Princeton) . Discrepancy Theory and Computational Geometry.
• 31 May 1996 Sanjeev Arora (Princeton). Polynomial-time Approximation Schemes for Euclidean TSP and other Geometric Problems.
• 30 May 1996 Laszlo Lovasz (Yale University). The delight of walking randomly.
• 11 April 1996 Christos Papadimitriou (UC Berkeley). Computational Approaches to Organization Theory.
• 25 January 1996 Andrew Yao (Princeton). An Overview of Quantum Cryptography.
• 1 December 1995 Frank Harary (New Mexico State University). Recent results on hypercube theory.
• 9 November 1995 Prabhakar Raghavan (IBM Almaden). Queueing theory without independence assumptions.
• 23 May 1995 N.G. de Bruijn
• 44. Springer Online Reference Works
a1, J. Barwise, Infinitary logic and admissible sets Doctoral Diss. Stanford (1967). a2, J. Barwise, Infinitary logic and admissible sets J.
http://eom.springer.de/B/b120180.htm
 Encyclopaedia of Mathematics B Article referred from Article refers to Beth definability theorem Definability theorems provide answers to the question to what extent implicit definitions can be made explicit. Questions of this kind are a traditional issue in mathematics, as is illustrated by the following examples. 1) Let be a polynomial over the real numbers having exactly one real root . Then the equation can be viewed as an implicit definition of , i.e. as a condition on a real number that involves and uniquely determines a number satisfying it, namely . The question whether there is an explicit definition of , i.e. a description of not involving itself, comes up to the question whether the implicit definition can be made explicit, say by representing the solution by radicals. Of course, an explicit definition of , say , can also be viewed as an implicit definition. In fact, this example mirrors the general experience that explicit definitions are special cases of implicit definitions. 2) Similarly to the above, one may consider a differential equation (cf. also

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