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1. JSTOR Interpolation, Preservation, And Pebble Games
Note how our theorem relates explicit definability of P in L to what may be Can we extend all standard interpolation and preservation theorems to<881:IPAPG>2.0.CO;2-K

2. Preservation Of Interpolation Features By Fibring -- Carnielli Et Al., 10.1093/l
The interest for such preservation results for combining logics is evident, Gabbay D, Maksimova L. Interpolation and definability Modal and
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Journal of Logic and Computation Advance Access published online on November 6, 2007
Journal of Logic and Computation, doi:10.1093/logcom/exm061
This Article Abstract Full Text (PDF) Alert me when this article is cited ... Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Add to My Personal Archive ... Request Permissions Google Scholar Articles by Carnielli, W. Articles by Sernadas, C.
Original papers
Preservation of Interpolation Features by Fibring
Walter Carnielli and Cristina Sernadas CLC and SQIG-IT, Department of Mathematics, IST, TU Lisbon, Portugal IFCH, UNICAMP, Brazil E-mail: Received 29 March 2006. Fibring is a metalogical constructor that permits to combine different logics by operating on their deductive systems under certain natural restrictions, as for example that the two given

3. Minimal Predicates, Fixed-points, And Definability
Minimal predicates, fixedpoints, and definability. Johan van Benthem J. Barwise and J. van Benthem Interpolation, preservation, and pebble games,
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    Minimal predicates, fixed-points, and definability
    Johan van Benthem Source: J. Symbolic Logic Volume 70, Issue 3 (2005), 696-712.
    PIA PIA PIA -conditions yields a language MIN(FO) equal in expressive power to LFP(FO), first-order logic closed under smallest fixed-points for monotone operations. As a concrete illustration of these notions, we show how our sort of predicate minimization extends the usual frame correspondence theory of modal logic, leading to a proper hierarchy of modal axioms: first-order-definable, first-order fixed-point definable, and beyond. Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text Links and Identifiers Permanent link to this document:

4. Johan Van Benthem : Current Teaching Activities
examples of nonmodal definability, syntax for preservation classes. Weeks 6 7 J. Barwise J. van Benthem, 1999, Interpolation, Preservation,
Advanced Modal Logic Philosophy 269, Spring 2003, Stanford, T 11-12, Th 11-12:30, 20-22K Abstract This course is a sequel to Philosophy 169, which was basically
an introduction to modal logic emphasizing major techniques,
plus a small tour of modern application areas. This time, we
present the mathematical theory behind modal logic. You need
some basic model theory for the results to be proved, but this
will be explained as we proceed. (And please ask questions.) Preliminary schedule Week 1
Basic modal language, translation, bisimulation invariance,
characterization theorem for the modal fragment of FOL Week 2
Guarded fragment and hybrid logics: expressive power
and decidability of suitable extended modal languages The counterpoint: undecidability of tiling problems, and
the sort of quantifier syntax which leads to undecidability. Week 3 Frame correspondence theory, Sahlqvist theorems Week 4 Connections with second-order logic, undefinability results Week 5 Basic completeness results and modal algebras Week 6 Modal algebras and frame representations

5. 03Cxx
03C35 Categoricity and completeness of theories; 03C40 Interpolation, preservation, definability; 03C45 Classification theory, stability and related
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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.)

6. Sachgebiete Der AMS-Klassifikation: 00-09
theories 03C40 Interpolation, preservation, definability 03C45 Stability and 03D65 Highertype and set recursion theory 03D70 Inductive definability
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

7. Mhb03.htm
03C40, Interpolation, preservation, definability. 03C45, Classification theory, stability and related concepts. 03C50, Models with special properties
03-XX Mathematical logic and foundations General reference works (handbooks, dictionaries, bibliographies, etc.) Instructional exposition (textbooks, tutorial papers, etc.) Research exposition (monographs, survey articles) Explicit machine computation and programs (not the theory of computation or programming) Proceedings, conferences, collections, etc. General logic Classical propositional logic Classical first-order logic Higher-order logic and type theory Subsystems of classical logic (including intuitionistic logic) Abstract deductive systems Decidability of theories and sets of sentences [See also Foundations of classical theories (including reverse mathematics) [See also Mechanization of proofs and logical operations [See also Combinatory logic and lambda-calculus [See also Logic of knowledge and belief Temporal logic ; for temporal logic, see ; for provability logic, see also Probability and inductive logic [See also Many-valued logic Fuzzy logic; logic of vagueness [See also Logics admitting inconsistency (paraconsistent logics, discussive logics, etc.)

8. MathNet-Mathematical Subject Classification
03C40, Interpolation, preservation, definability. 03C45, Stability and related concepts. 03C50, Models with special properties (saturated, rigid, etc.)

9. HeiDOK
03C40 Interpolation, preservation, definability ( 0 Dok. ) 03C45 Classification theory, stability and related concepts ( 0 Dok.

10. List KWIC DDC22 510 And MSC+ZDM E-N Lexical Connection
definability inductive 03D70 definability interpolation, preservation, 03C40 definability other notions of settheoretic 03E47
curriculum development # goals of mathematics teaching.
curriculum guides, official documents # syllabuses.
curriculum materials, effective teaching, etc.) # teaching and curriculum (innovations, teaching practices, studies of
curvature # minimal surfaces, surfaces with prescribed mean
curvature manifolds # negative
curvature manifolds # positive
curvature restrictions # methods of Riemannian geometry, including PDE methods;
curvature, tight, etc.) # immersions (minimal, prescribed
curve fitting # smoothing,
curve sketching, extremum problems) # differential calculus (e.g.:
curved groups # hyperbolic groups and nonpositively curved space backgrounds # quantum field theory on curves curves curves # directly differentiable curves # elliptic curves # geometry of orders of nondifferentiable curves # plane and space curves # pseudoholomorphic curves and curves of low genus # special curves and surfaces on projective and affine planes curves and surfaces) # computer aided design (modeling of curves and their moduli # vector bundles on curves in Euclidean space curves of low genus # special curves and curves over finite and local fields curves over global fields # elliptic curves over local fields # elliptic curves) # convex sets in $2$ dimensions (including convex curves, singular points, limit cycles # location of integral

11. The Journal Of Symbolic Logic, Volume 64
825845 BibTeX Alexandru Baltag Interpolation and Preservation for Pebble Ieke Moerdijk An Elementary definability Theorem for First Order Logic.
The Journal of Symbolic Logic , Volume 64
Volume 64, Number 1, March 1999

12. Logic Colloquium 2003
the relations between some of these notions and nonstandard versions of the standard logical results of interpolation, preservation and definability.
Main Awards Registration Accommodation ... ASL
Speakers and Titles
Tutorial speakers
Michael Benedikt Model Theory and Complexity Theory
Bell Labs, Lisle, USA.
E-mail: ABSTRACT: This tutorial concentrates on links between traditional (infinitary) model theory and complexity theory. We begin with an overview of the `classical' connection between complexity theory and finite model theory, giving quickly the basic results of descriptive complexity theory. /We then discuss several ways of generalizing this to take account a fixed infinite background structure. We will start by giving the basics of complexity theory parameterized by a model (algebraic complexity over an arbitrary structure). We then cover results characterizing first-order theories of models via the complexity of query problems (embedded finite model theory). Finally, time permitting, we will look at abstractions of descriptive complexity theory to take into account a background structure. Stevo Todorcevic Set-Theoretic Methods in Ramsey Theory
C.N.R.S. - UMR 7056, Paris, France.

13. Search Results For "interpolation" – FacetedDBLP
3, Larisa Maksimova definability and Interpolation in NonClassical Logics. Search with DBLP WebCrawler Search on Bibsonomy

14. DBLP: Johan Van Benthem
30 Jon Barwise, Johan van Benthem Interpolation, Preservation, and Pebble Games. J. Symb. Log. 8, Johan van Benthem Notes on Modal definability.
Johan van Benthem
List of publications from the DBLP Bibliography Server FAQ Coauthor Index - Ask others: ACM DL ACM Guide CiteSeer CSB ... Balder ten Cate , Johan van Benthem, : Lindstrom theorems for fragments of first-order logic. LICS 2007 EE Johan van Benthem, Eric Pacuit : The Tree of Knowledge in Action: Towards a Common Perspective. Advances in Modal Logic 2006 EE Johan van Benthem, Jan van Eijck Barteld P. Kooi : Logics of communication and change. Inf. Comput. 204 EE Johan van Benthem: Modal Frame Correspondences and Fixed-Points. Studia Logica 83 EE Johan van Benthem, Guram Bezhanishvili Balder ten Cate Darko Sarenac : Multimo dal Logics of Products of Topologies. Studia Logica 84 EE Johan van Benthem: An Essay on Sabotage and Obstruction. Mechanizing Mathematical Reasoning 2005 EE Johan van Benthem, Jan van Eijck Barteld P. Kooi : Common knowledge in update logics. TARK 2005 Johan van Benthem: Open Problems in Logic and Games. We Will Show Them! (1) 2005 EE Johan van Benthem: Guards, Bounds, and Generalized Semantics. Journal of Logic, Language and Information 14 EE Marco Aiello , Johan van Benthem, Guram Bezhanishvili : Reasoning About Space: The Modal Way.

15. A Report On LACS A Tribute To Helena Rasiowa Logic, Algebra And
He gave two talksone on interpolation, preservation and pebble games, Invariant definability in infinite and finite model theory Janos Makowsky
A Report on LACS : a tribute to Helena Rasiowa
Logic, Algebra and Computer Science. Helena Rasiowa
A Minisemester at Warsaw, December 222, 1996.
Mohua Banerjee
Machine Intelligence Unit, Indian Statistical Institute, Calcutta E-mail:
The atmosphere was easy-unlike that in a standard conference-and the long span of the meeting gave one a lot of scope for academic interaction. Quite a few participants were close associates/students of Rasiowa, and so during conversations, one caught glimpses of the great personality as well. It was a privilege to be a part of the assembly and also, to present our work on rough logic that follows Rasiowa's style of investigation. The participants were accommodated either at the Banach Center, or hotels of the University of Warsaw, and the organizers took great care to see to the comfort of each one (in particular that none froze!). In general too, considering the extremely hard time that the Polish are going through, one was amazed at the warmth exuded and help extended, even by the common person on the street. Among the audience, we had a number of bright young students (Polish, and others), shooting questions, and enjoying the proceedings. I remember a nice evening with some of them, trudging through the ice to a concert at the renowned Chopin School of Music, and then being amply rewarded by the concert itself-three well-performed piano concertos by students of the School. We also had long exchanges about the problems in our countries, specially those in the academic spheres. There did not seem to be many differences.

16. USC, Department Of Mathematics, Graduate Courses
or consent of department) Interpolation and approximation of functions, .. interpolation and definability; preservation theorems; ultraproducts.
Course Descriptions (MATH)
  • 511Probability. [ = STAT 511] (3) (Prereq: MATH 241 with a grade of C or higher) Probability and independence; discrete and continuous random variables; joint, marginal, and conditional densities, moment generating functions; laws of large numbers; binomial, Poisson, gamma, univariate, and bivariate normal distributions.
  • 520Ordinary Differential Equations. (3) (Prereq: MATH 544 or 526; or consent of department) Differential equations of the first order, linear systems of ordinary differential equations, elementary qualitative properties of nonlinear systems.
  • 521Boundary Value Problems and Partial Differential Equations. (3) (Prereq: MATH 520, or 241 and 242) Laplace transforms, two-point boundary value problems and Green's functions, boundary value problems in partial differential equations, eigenfunction expansions and separation of variables, transform methods for solving PDE's, Green's functions for PDE's, and the method of characteristics.
  • (Prereq: MATH 544 or 526 or consent of instructor) Basic principles and methods of Fourier transforms, wavelets, and multiresolution analysis; applications to differential equations, data compression, signal and image processing; development of numerical algorithms. Computer implementation.

17. Qualifying Exam Syllabi
categoricity, interpolations, definability and preservation theorems. piecewise interpolation, eigenvalue problems, and numerical integration.
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: 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.

18. General General Mathematics Mathematics For Nonmathematicians
of theories Interpolation, preservation, definability Classification theory, stability and related concepts Models with special properties (saturated,

Prototypical and ideal cases 2.2.3 Extreme cases and interpolation 2.2.4 development 5.1.4 A remark on definability preservation and modal logic 5.2
List of Publications
All files are Latex source, unless said otherwise (and draft versions).
(January 4, 2005)
Books, published or accepted
A preliminary version is available via:
(The Technical Report Series)

(The Report)
Part 0

Part 1
Part 7
Articles in international journals, published or accepted
[LMS01] D.Lehmann, M.Magidor, K.Schlechta: "Distance Semantics for Belief Revision", Journal of Symbolic Logic, Vol.66, No. 1, March 2001, p. 295-317 Abstract: A vast and interesting family of natural semantics for belief revision is defined. Suppose one is given a distance d between any two models. One may then define the revision of a theory K by a formula alpha as the theory defined by the set of all those models of alpha that are closest, by d, to the set of models of K. This family is characterized by a set of rationality postulates that extends the AGM postulates. The new postulates describe properties of iterated revisions.
[SD01] K.Schlechta, J.Dix: "Explaining updates by minimal sums", Theoretical Computer Science, 266 (2001), pp. 819-838 Abstract: Human reasoning about developments of the world involves always an assumption of inertia. We discuss two approaches for formalizing such an assumption, based on the concept of an explanation: (1) there is a general preference relation given on the set of all explanations, (2) there is a notion of a distance between models and explanations are preferred if their sum of distances is minimal. We show exactly under which conditions the converse is true as well and therefore both approaches are equivalent modulo these conditions. Our main result is a general representation theorem in the spirit of Kraus, Lehmann and Magidor.

20. ILLC Publications, Mathematical Logic And Foundations (ML) Series
ML1994-12 Victor Selivanov Fine Hierarchy and definability in the Lindenbaum ML-1996-12 Jon Barwise, Johan van Benthem Interpolation, Preservation,

21. 361/369 (Total 5522) NO 122 03C70 Logic On
Translate this page 111, 03C40, Interpolation, preservation, definability. 110, 03C35, Categoricity and completeness of theories. 109, 03C30, Other model constructions

22. University Graduate School Bulletin 2000-2002: Mathematics
theory of undecidability and implicit definability, Gödel’s theorems on completeness and modelcompleteness, interpolation, preservation and
Academic Bulletin

University Graduate School

Kirkwood Hall 111
Indiana University
Bloomington, IN 47405
Contact Graduate Office

Mathematics Graduate Faculty
Special Departmental Requirements
Master of Arts Degree Master of Arts for Teachers Degree ... Courses College of Arts and Sciences Bloomington Chairperson Professor Daniel Maki Graduate Faculty College Professor Roger Temam Distinguished Professor Ciprian Foias Professors Steen Andersson, Goro Azumaya (Emeritus), S. Thomas Bagby, Eric Bedford, Grahame Bennett, Hari Bercovici, Rabi Bhattacharya, Richard Bradley, John Brothers, Arlen Brown (Emeritus), John Challifour (Physics), Jiri Dadok, James Davis, Vinay Deodhar, Allan Edmonds, Robert Glassey, Victor Goodman, Darrell Haile, David Hoff, Jan Jaworowski (Emeritus), Andrew Lenard (Emeritus, Physics), Charles Livingston, Morton Lowengrub (Emeritus), Russell Lyons, Daniel Maki, Kent Orr, Sergey Pinchuk, Madan Puri, Billy Rhoades (Emeritus), George Springer (Emeritus, Computer Science), Joseph Stampfli (Emeritus), Peter Sternberg, Maynard Thompson, Alberto Torchinsky, Lanh Tran, William Ziemer, Kevin Zumbrun Associate Professors Scott Brown, Marlies Gerber, William Gustin (Emeritus), Michael Jolly, Paul Kirk, Jee Heub Koh, Michael Larsen, Valery Lunts, Robert MacKenzie (Emeritus), Lawrence Moss, Ji-Ping Sha, Bruce Solomon, Shouhong Wang,* William Wheeler, Yuxi Zheng

23. Martin Goldstern's Papers
This paper looks at interpolation from a more general point of view is a monotone family of measure zero sets (with some nice definability properties).
Martin Goldstern's Papers
This page is supposed to contain a list of all my mathematical papers (about 2 dozen of them) with links to tex/dvi/ps files, plus abstracts, bibliographical references, and perhaps more. For the moment, here are only a bibtex file , and a few papers:
  • In April 2000 I gave a talk Mengenlehre: Hierarchie der Unendlichkeiten pdf dvi and Postscript files are also available.)
  • The recent paper: Clones on regular cardinals was written jointly with Saharon Shelah. Also A clone on a set A is a family of finitary functions which contains all the projections and is closed under composition. (In other words: the set of term functions of some universal algebra over A.)
    The family of all clones on a given set A forms a complete algebraic lattice. Many interesting things are known about this lattice if A is finite (for example a classification of all coatoms), but much less is known for infinite sets A.
    We investigate various families of coatoms in this lattice; it turns out that if the cardinality of A is weakly compact, then a nice structure can be found, and in (almost) all other cases we can show a "nonstructure" result.
  • A paper on uniform distribution: Metric, fractal dimensional and Baire Results on the Distribution of Sequences and Subsequences

24. Coherent Systems, 2 - Elsevier
Prototypical and ideal cases 2.2.3 Extreme cases and interpolation 2.2.4 4.3.2 The results CHAPTER 5 definability PRESERVATION 5.1 Introduction
Home Site map Elsevier websites Alerts ... Coherent Systems, 2 Book information Product description Audience Author information and services Ordering information Bibliographic and ordering information Conditions of sale Book-related information Submit your book proposal Other books in same subject area About Elsevier Select your view COHERENT SYSTEMS, 2
To order this title, and for more information, click here
Karl Schlechta
, K. Schlechta Universite de Provence and Laboratoire d'Informatique Fondamentale (CNRS UMR 6166), Marseille, France
Included in series
Studies in Logic and Practical Reasoning, 02

One aspect of common sense reasoning is reasoning about normal cases, e.g. a physician will first try to interpret symptoms by a common disease, and will take more exotic possibilities only later into account. Such "normality" can be encoded, e.g. by a relation, where case A is considered more normal than case B. This gives a standard semantics or interpretation to nonmonotonic reasoning (a branch of common sense reasoning), or, more formally, to nonmonotonic logics. We consider in this book the repercussions such normality relations and similar constructions have on the resulting nonmonotonic logics, i.e. which types of logic are adequate for which kind of relation, etc. We show in this book that some semantics correspond nicely to some logics, but also that other semantics do not correspond to any logics of the usual form.
Libraries and researchers in nonmonotonic and related logics

25. MathGuide - OPAC Subject Catalog
03C40 Interpolation, preservation, definability; 03C45 Classification theory, 46M35 Abstract interpolation of topological vector spaces
Browse the GBV OPAC by MSC 2000
This is a browse interface to the union catalogue of the Common Library Network GBV based on the MSC 2000 classification.
You can browse down to the individual notation, the links available will direct you to the appropriate place in the GBV OPAC, which uses a notation related to, but different from MSC.
Note: Not all books available are contained in the online catalogue. Please use the Goettingen State University Library's Alphabetical Catalogue to search for monographs, dissertations and journals missing in the OPAC. Open all categories Close all categories
  • Foundations
    • 00-XX General
      • Instructional exposition (textbooks, tutorial papers, etc.)
      • Research exposition (monographs, survey articles)
      • General mathematics
      • General and miscellaneous specific topics
        • General mathematics
        • Mathematics for nonmathematicians (engineering, social sciences, etc.)
        • Problem books
        • Recreational mathematics
        • Bibliographies
        • External book reviews
        • Dictionaries and other general reference works
        • Formularies
        • Philosophy of mathematics
        • Methodology of mathematics, didactics

26. - Mathematics Courses
Model theory compactness theorem; Lowenheim/Skolem theorems; definability; ultraproducts; preservation theorems; interpolation theorems.
Mathematics Courses
Lower Division Courses
1. Precalculus. Lecture, three hours; discussion, one hour. Preparation: three years of high school mathematics. Requisite: successful completion of Mathematics Diagnostic Test. Function concept. Linear and polynomial functions and their graphs, applications to optimization. Inverse, exponential, and logarithmic functions. Trigonometric functions. P/NP or letter grading. 2. Finite Mathematics. Lecture, three hours; discussion, one hour. Preparation: three years of high school mathematics. Finite mathematics consisting of matrices, Gauss/Jordan method, combinatorics, probability, Bayes theorem, and Markov chains. P/NP or letter grading. 3A. Calculus for Life Sciences Students. Lecture, three hours; discussion, one hour. Preparation: three and one-half years of high school mathematics (including trigonometry). Requisite: successful completion of Mathematics Diagnostic Test or course 1 (C - or better). Not open for credit to students with credit in another calculus sequence. Techniques and applications of differential calculus. Introduction to the integral. P/NP or letter grading. 3B. Calculus for Life Sciences Students. Lecture, three hours; discussion, one hour. Requisite: course 3A (C - or better). Techniques and applications of integral calculus, logarithmic and exponential functions, introduction to differential equations. P/NP or letter grading.

27. 1991 Mathematics Subject Classification (MSC 1991)
03C40 Interpolation, preservation, definability; 03C45 Stability and related 03E45 Constructibility, ordinal definability, and related notions
1991 Mathematics Subject Classification (MSC 1991)
  • Instructional exposition (textbooks, tutorial papers, etc.)
  • Research exposition (monographs, survey articles)
    General and miscellaneous specific topics
  • General mathematics
  • Mathematics for nonmathematicians (engineering, social sciences, etc.)
  • Problem books
  • Recreational mathematics
  • Bibliographies
  • Dictionaries and other general reference works
  • Formularies
  • Methodology of mathematics, didactics
  • Theory of mathematical modeling
  • General methods of simulation
  • Dimensional analysis
  • Physics (use more specific entries from Sections 70 through 86 when possible)
  • Miscellaneous topics
    Conference proceedings and collections of papers
  • Collections of abstracts of lectures
  • Collections of articles of general interest
  • Collections of articles of miscellaneous specific content
  • Proceedings of conferences of general interest
  • Proceedings of conferences of miscellaneous specific interest
  • Festschriften
  • Volumes of selected translations
  • Miscellaneous volumes of translations
  • 01-XX
  • General reference works (handbooks, dictionaries, bibliographies, etc.)

28. Notre Dame Journal Of Formal Logic, 1998; 39 (2)
Interpolation and Preservation in M Lw1 / Sturm, Holger, 190211 Note on Supervenience and definability / Humberstone, Lloyd, 243-252
Sumario Título / Autor(es) Página(s) Reverse Mathematics and Fully Ordered Groups / Solomon, Reed Interpolation and Preservation in M Lw1 / Sturm, Holger Intuitionistic Open Induction and Least Number Principle and the Buss Operator / Ardeshir, Mohammad Moniri, Mojtaba The Laws of Distribution for Syllogisms / Hodges, Wilfrid Duality and Completeness for US-Logics / Bellissima, Fabio Cittadini, Saverio Note on Supervenience and Definability / Humberstone, Lloyd Failure of Interpolation in Combined Modal Logics / Marx, Maarten Areces, Carlos On a Consistent Subsystem of Frege's Grundgesetze / Burgess, John P Book Review: - Correspondence and Disquotation: An Essay on the Nature of Truth / David, Marian Yaqub, Aladdin M

29. CIS-Bibliothek - Institutsberichte
Johan van Benthem, Modality, Bisimulation and Interpolation in Infinitary Logic Eva Hoogland, Algebraic Characterization of Various Beth definability
CIS-Bibliothek - Institutsberichte
Autor Titel Reihe/Nr Jahr H.J.Verkuyl and A.Bende-Farkas On Hungarian Noun Phrase Structure uil-ots-97-003/TL-CL H.J.Verkuyl Events as Dividuals: Aspectual Composition and Event Semantics uil-ots-97-004/TL-CL R.Backofen Expressivity and Decidability of First-Order Languages over Feature Trees Diss. Renate Bartsch Understanding Understanding ILLC-LP-96-01 Rens Bod and Remko Scha Data-Oriented Language Processing: An Overview ILLC-LP-96-13 Renate Bartsch Propositional Attritudes in Dynamic Conceptual Semantics ILLC-LP-96-11 Peter van Emde Boas The Convenience of Tilings ILLC-CT-96-01 Michael van Lambalgen and Jaap van der Does A Logic of Vision ILLC-LP-96-14 Paul Dekker Reference and Representation ILLC-LP-96-12 Jelle Gerbrandy and Willem Groeneveld Reasoning about Information Change ILLC-LP-96-10 Jaap van der Does, Willem Groeneveld and Frank Veltman An Update of MIGHT ILLC-LP-96-09 A.S.Troelstra From Constructivism to Computer Science ILLC-CT-96-02 Lex Hendriks Intuitionistic Propositional Logic with only Equivalence has no Interpolation ILLC-ML-96-13 Hiroakira Ono Decidability and finite model property of substructural logics ILLC-ML-95-09 Kees Doets Proper Classes ILLC-ML-96-04 Hajnal Andreka, Johan van Benthem and Istvan Nemeti

30. Logic Seminar - Archive
definability of regular languages in firstorder logic Feasible disjunction and interpolation properties in modal logic S4 May 27, 2002 at 13.oo
Logic seminar: archive 1995 - 2006
  • S. Riis (Aarhus)
    Symmetrical equations -> symmetrical solutions?
  • A. Woods (Australia)
    Random finite functions standard and nonstandard

    January 4, 1996
  • J. Hruska (Charles University)
    Open-point a Open-open hry na regularnich topologickych prostorech a jejich ekvivalenty na Booleovskych algebrach
    March 25, 1996
  • Dan Willard (SUNY, Albany)
    Introspective Semantics for Turing Machine Languages

    March 4, 1996
  • Yuri Gurevich (Ann Arbor) Finite model theory June 17, 1996
  • Stevo Todorcevic (Toronto) Borel chromatic numbers July 10, 1996
  • L. van den Dries (Urbana) O-minimal extensions of R and quantifier elimination with Exp July 15, 1996
  • A. Sochor (MU) Nestandartnost nadmodelu September 16, 1996
  • A. Sochor (MU) Nestandartnost nadmodelu II. September 30, 1996
  • A. Sochor (MU) Nestandartnost nadmodelu III. October 7, 1996
  • P. Pudlak (MU) O Dawkingskove knize "Selfish gene" October 21, 1996
  • J. Krajicek (MU) Forcing v jazyce teorie miry November 11, 1996
  • J. Krajicek (MU) Spodni odhad pro polynomialni kalkulus podle A.A.Razborova December 2, 1996
    The Substructure Preservation Theorem fails in the case of finite Interpolation and definability for polynomial time logic According to ~1,
    THE UNIVERSITY OF MICHIGAN COMPUTING RESEARCH LABORATORY TOWARDI LOGIC TAILORED FOR COMPUTA''TIONALI COM PILXITY Yuri Gurevich CRL-TR-3-64 JAN UARY 1984 Room 1079. East Engineering Building Ann Arbor, Michigan 4-8109 USA Tel: (313) 763-8000 37 I have also checked that Theorem 1 remains true in the case of finite structures if 4 is an cxistential sentence, a universal sentence, a prenex sentence with prefix n3 or a prenex sentence with prefix n V Andreas Blass observed that if ~(P) is positive (resp. monotone, monotone on finite structures) in P then so is q(-)P). Thus, if Theorem 1 is true inthe finite case for prenex sentences 4 with certain prefixes then it is true in the finite case for prenex sentences with the dual prefixes. [UZ] J.D. Ullman, "Principles of Database Systems", Computer Science Press, 1982. [Vap] L.G. Valiant, "Relative Complexity of Checking and Evaluating", Information Processing 5 (1976), 20-23. [Va] M.Y. Vardi, "Complexity of Relational Query Languages", Proc. of 14th ACM Symposium on Theory of Computing, 1982, 137-146. [Zf] M.M. Zloof, "Query-by-Example: a Database Language", IBM Syst. Journal 16 (1977), 324-343. UNIVERSITY OF MICHIGAN 3 9015 03026 8059 3 9015 03026 8059

    32. USC: Academic Bulletins
    {=CSCE 561} (3) (Prereq MATH 242 or 520) Interpolation and approximation of .. interpolation and definability; preservation theorems; ultraproducts.
    Skip Navigation USC THIS SITE updated 8/15/2007 Mathematics
    Jerrold R. Griggs , Chair Professors
    Colin Bennett, Ph.D., University of Newcastle upon Tyne, 1971
    Susanne C. Brenner, Ph.D., University of Michigan, 1988
    Stephen J. Dilworth, Ph.D., Cambridge University, 1985
    Michael A. Filaseta, Ph.D., University of Illinois, 1984
    Maria Girardi, Ph.D., University of Illinois, 1990
    Jerrold R. Griggs, Ph.D., Massachusetts Institute of Technology, 1977
    Ralph E. Howard, Ph.D., California Institute of Technology, 1982
    Andrew R. Kustin, Ph.D., University of Illinois, 1979
    George F. McNulty, Ph.D., University of California, Berkeley, 1972

    33. Googlelinked Mathematics Subject Headings
    03C40 Interpolation, preservation, definability 03C45 Classification theory, stability and related concepts 03C50 Models with special properties (saturated,
    mathematics googlelinks how it works
    [This page is a work in progress, started 25 June 2004. I'm still figuring out how to automate the creation of this page in the best way, but the great thing is that Google will keep it up to date for me when I'm done!]
    Googlelinked Mathematics Subject Headings
    All links dereference through Google's "I'm feeling Lucky."
    Here's an explanation of what I'm trying to do here.
    00–01 Instructional exposition ( textbooks , tutorial papers, etc.)
    00–02 Research exposition ( monographs survey articles
    00Axx General and miscellaneous specific topics
    General mathematics
    00A06 Mathematics for nonmathematicians (engineering, social sciences, etc.) Problem books Recreational mathematics [See also 97A20] Bibliographies 00A17 External book reviews Dictionaries and other general reference works Formularies Philosophy of mathematics [See also 03A05] 00A35 Methodology of mathematics, didactics [See also 97Cxx, 97Dxx] 00A69 General applied mathematics 00A71 Theory of mathematical modeling 00A72 General methods of simulation Dimensional analysis 00A79 Physics (use more specific entries from Sections 70-86) 00A99 Miscellaneous topics 00Bxx Conference proceedings and collections of papers 00B05 Collections of abstracts of lectures 00B10 Collections of articles of general interest 00B15 Collections of articles of miscellaneous specific content 00B20 Proceedings of conferences of general interest 00B25 Proceedings of conferences of miscellaneous specific interest

    34. MSC 2000 : CC = T
    03C40 Interpolation, preservation, definability; 03C45 Classification theory, 46M35 Abstract interpolation of topological vector spaces See also

    35. Kit Fine And The Ontology Of Modal Actualism
    It is shown that Beth s definability theorem and its corollary, the interpolation lemma, fail for quantified S5, with or without constant domain,
    Home Site Map
    Living Ontologists
    Kit Fine and the Ontology of Modal Actualism
    INTRODUCTION "My aim in this paper is to help lay the conceptual and methodological foundations for the study of realism. I come to two main conclusions: first, that there is a primitive metaphysical concept of reality, one that cannot be understood in fundamentally different terms; and second, that questions of what is real are to be settled upon the basis of considerations of ground. The two conclusions are somewhat in tension with one another, for the lack of a definition of the concept of reality would appear to stand in the way of developing a sound methodology for determining its application; and one of my main concerns has been to show how the tension between the two might be resolved. The paper is in two main parts. In the first, I point to the difficulties in making out a metaphysical conception of reality. I begin by distinguishing this conception from the ordinary conception of reality (§ 1) and then show how the two leading contenders for the metaphysical conception - the factual and the irreducible - both appear to resist formulation in other terms. This leads to the quietist challenge, that questions of realism are either meaningless or pointless (§4); and the second part of the paper (§§5-10) is largely devoted to showing how this challenge might be met. I begin by introducing the notion of ground (§5) and then show how it can be used as a basis for resolving questions both of factuality (§§6-7) and of irreducibility (§§8-9). I conclude with some remarks on the essential unity of these two questions and of the means by which they are to be answered (§ 10)."

    36. Holger Sturm
    Translate this page of Philosophical Logic 30 (2001), S. 571-590; Global definability in modal logic (mit M. de Rijke). Interpolation and preservation in ML_omega_1.
    Home Philosophie in Konstanz Lehre Forschung Mitarbeiter Fachschaft Termine Links Internetseiten ... Wolters, Gereon Holger Sturm Adressen Dienstlich:
    Fachgruppe Philosophie
    78457 Konstanz
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    78465 Konstanz
    Tel.: (07531) 384655 Schwerpunkte in Forschung und Lehre
    • Analytische Ontologie Erkenntnistheorie
      Logik (speziell: Modallogik, Temporallogik, Epistemische Logik, Philosophie der Logik) Philosophie des Geistes
      Sprachphilosophie Britischer Empirismus
    Work in Progress
    • Understanding Sellars' Looks-Talk Intrinsische Eigenschaften War Hume kausaler Realist?
    • Reduktion und Supervenienz. In: W. Spohn, P. Schroeder-Heister, E. Olsson (Hrsg.) : Logik in der Philosophie, Synchron, Heidelberg, S. 305-336. Russell's paradox and our conception of properties, or: Why semantics is no proper guide to the nature of properties. In: G. Link (Hrsg.): One Hundred Years of Russell's Paradox, de Gruyter, Berlin, S. 591-609. (mit V. Halbach)

    37. 6th Panhellenic Logic Symposium :: Programme
    Among classical theorems of model theory, preservation theorems are results of Ackermann Lemma with applications to modal ìdefinability; 1155-1220
    6th Panhellenic Logic Symposium
    Volos, Greece, 5-8 July 2007
    Thursday 5.7.07
    Registration - Opening
    Constantine Tsinakis (Vanderbilt University):
    Algebraic Methods in Logic Algebraic logic studies classes of algebras that are related to logical systems, as well as the process by which a class of algebras becomes the algebraic counterpart (semantics)" of a logical system. A field practitioner usually approaches the solution of a problem in logic by first reformulating it in the language of algebra; then by using algebra to solve the reformulated problem; and lastly by expressing the result into the language of logic. A representative association of the preceding kind is the one between the class of Boolean algebras and classical propositional calculus.
    The focus of this talk is substructural logics and their algebraic counterparts. Substructural logics are non-classical logics that are weaker than classical logic, in the sense that they lack one or more of the structural rules of contraction, weakening and exchange in their Genzen-style axiomatization. (It is, however, convenient to think of the classical logic and intuitionistic logic as substructural logics.) These logics encompass a large number of non-classical logics related to computer science (linear logic), linguistics (Lambek Calculus), philosophy (relevant logics), and multi-valued reasoning.
    The following are among the objectives of the talk:
    Propose a uniform framework for the study of the algebraic counter-parts of substructural propositional logics. These algebras, referred to as residuated lattices, have a recently discovered rich structure theory. (Note: The term "residuated lattice" has been used in the literature to refer to algebras that are integral, commutative and bounded. This class and its subclasses are not sufficiently general to provide semantics for all substructural logics.)

    38. Model Theory - Elsevier
    Preservation Theorems. Applications of Special Models to the Theory of definability. Applications to Field Theory. Application to Boolean Algebras.

    39. Logic Colloquium 2006
    Byunghan Kim, Stable definability and generic relations; Alexei Kolesnikov, Generalized types .. Larisa Maksimova, Weak interpolation in equational logic
    main invited contributed registration how to get there
    Contributed Talks
    This page contains the schedule and abstracts of the contributed talks at the Logic Colloquium 2006
    The talks are 15 minutes + 5 minutes for questions. The following facilities will be available in each room:
    • Beamer Laptop (for people who did not bring their own laptop: possible file formats .pdf .ps .ppt) Overhead projector Black board or white board
    At your convenience you can send a .pdf file with your slides to Jasper Stein ( ) who will have it pre-installed on the presentation computer.
    Room 2
    Room 2
    Room 2
    • Vadim Puzarenko

    40. Institutions
    Logical results obtained include very general versions of Craig interpolation, Robinson consistency, Beth definability, and Herbrand universe theorems;
    Institutions 1. Motivation The enormous and still growing diversity of logics used in computer science presents a formidable challenge. One approach to bringing some order to this chaos is to formalize the notion of "a logic" and then systematically study general properties of logics using this formalization, including the representation, implementation, and translation of logics. This is the purpose of the theory of institutions , as developed and applied in a literature that now has hundreds of papers. The original application of institutions defined powerful mechanisms for structuring theories over any logical system; this was applied in the module systems of languages in the OBJ family , including BOBJ, CafeOBJ, Maude, CASL, and OBJ3, each of which has a different logic, under the name "parameterized programming," and it was later extended to module systems for programming languages. The module systems of Ada, C++, Lotos, and ML were all influenced by these ideas, which are most nearly fully implemented in the so-called signatures, structures, and functors of SML. Institutions have also been applied to the semantics of databases and ontologies, e.g. for the semantic web. Here the main contribution of institutions is to formalize the notion of translation from one logic to another in such as way as to preserve truth, and to provide a number of basic results about such translations, such as when they preserve the modular structure of an ontology; see

    41. Group In Logic And The Methodology Of Science -
    compactness theorem, preservation theorems, LöwenheimSkolem theorems, of universal classes, interpolation and Beth’s definability theorem.
    Requirements for the Ph.D. Program
    As in most Ph.D. programs at Berkeley, the work in this program is divided into two phases. In the first, the student acquires a fairly broad but rigorous working knowledge in three areas. His or her competence in these areas is tested in a two-part comprehensive Preliminary Examination and a Qualifying Examination. Part I of the Preliminary Examination deals with the foundations of mathematics (including elements of model theory, recursion theory, and incompleteness and undecidability results). Part II concerns one of the following areas of philosophy: philosophy of science, philosophy of language, philosophy of mathematics, or philosophical logic. The Qualifying Examination covers material from a mathematics option, a philosophy option, or a special option (for details, see Preliminary Examination and Qualifying Examination below). In the second phase of the Ph.D. program, after having passed the Qualifying Examination, the student selects a Dissertation Supervisor and, under his or her guidance, carries out original research and writes a dissertation. Since most of the faculty have strong interests in logic, students wishing to work in some other area of the methodology of science may find difficulty in finding a Dissertation Supervisor unless they propose to approach their problems using the methods of mathematics and logic.
    Advancement to Candidacy
    For advancement to candidacy for the Ph.D. degree, the student must complete the requirements described in

    42. SUB Göttingen - Systematische Recherche Im Katalog Der SUB
    EADC 400, Interpolation, preservation, definability EADE 450, Inner models, including constructibility, ordinal definability, and core models

    43. MPLA :: Graduate Program In Logic, Algorithms And Computation
    From Birkhoff axiomatizability to interpolation a categorical modeltheoretic approach. . Theory of definability and completeness in Modal Logic.
    Graduate Program in Logic, Algorithms and Computation. Old website
    By Semester
    • A. Tzouvaras University of Thessaloniki
      On the consistency of NF E. Kranakis Carleton University (Ottawa)
      The power of tokens: Rendezvous and symmetry detection for twomobile agents in a ring K. Potika N.T.U.A.
      Boundary labeling problems
      Petri net semantics for communicating agents D. Thilikos University of Athens
      Graph searching in a crime wave (joint work with D. Richerby) Y. Moschovakis
      Borel determinacy A. Kechris Caltech
      Set theory and dynamical systems E. Zachos N.T.U.A.
      Hierarchies of complexity classes
    • K. Yamazaki Gunma University (Japan).
      Relationships between the class of unit grid intersection graphs and other classes of bipartite graphs. H. Schwichtenberg University of Munich.
      Logic for computable functionals and their approximations. Y. Moschovakis "... (a+bn)/n=x, hence God exists" — with Logic only! D. Richerby M.P.L.A. How to kill a Minotaur: An introduction to graph searching. Ch. Kapoutsis

    44. Ultraproducts And Possible Worlds Semantics In Institutions
    Diaconescu, R., An institutionindependent proof of Craig Interpolation Theorem. Petria, M. and Diaconescu, R., Abstract Beth definability in

    45. Õëéêü ÌáèçìÜôùí - Courses
    Interpolation and polynomial approximation. . definability and arithmetical hierarchy. Turing reducibility and degrees of unsolvability.
    Home Page Contact Info Site Map Greek Version www
    Undergraduate Course Contents
    • Core Requirements
    • Discrete Mathematics
      Sets. Relations. Functions. Natural Numbers. Mathematical Induction. Countability of sets. Propositional calculus. Set operations and logical connectives. Boolean algebra. Theorems and proofs. Types of proofs. Basic counting principles. Permutations. Combinations. The inclusion-exclusion principle. Graphs. Isomorphic graphs. Paths, cycles and connectivity in graphs. Matrices of graphs. Directed graphs. Trees. The optimal spanning tree problem. Rooted trees. Eulerian trails and Hamilton cycles. Planar graphs and graph coloring. Linear recurrence relations with constant coefficients. Introduction to Computer Science
      Algorithms and computer programming principles: basic logic, modularity, sequencing, selection and iteration, recursion, parallelism, data structures. Theory of algorithms: computability, grammars, complexity. Computer architecture: logic gates, instruction execution, memory, machine architecture, machine language, parameter passing, input/output devices. Programming languages: grammars, syntax analysis (parsing), translators (interpreters and compilers). Operating systems, file systems, and databases. Computer networks.

    46. Publications
    It is shown how this single new interpolation theorem unifies a number of related results namely, the classical preservation theorems concerning
    Modal Characterisation Theorems over Special Classes of Frames , with A. Dawar
    Preprint of extended and corrected journal version of LICS 2005 paper , 2007, 48 pages. Abstract The Boundedness Problem for Monadic Universal First-Order Logic
    Proceedings of 21th IEEE Symposium on Logic in Computer Science LICS 2006, pp 37-46. Abstract Consider the monadic boundedness problem for least fixed points over FO formulae as a decision problem: Given a formula that is positive in $X$, decide whether there is a uniform finite bound on the least fixed point recursion based on this formula. Few fragments of FO are known to have a decidable boundedness problem; boundedness is known to be undecidable for many fragments. We here show that monadic boundedness is decidable for purely universal FO formulae without equality in which each non-recursive predicate occurs in just one polarity (e.g., only negatively). The restrictions are shown to be essential: waving either the polarity constraint or allowing positive occurrences of equality, the monadic boundedness problem for universal formulae becomes undecidable. The main result is based on a model theoretic analysis involving ideas from modal and guarded logics and a reduction to the monadic second-order theory of trees. Modal Characterisation Theorems over Special Classes of Frames , with A. Dawar

    47. DoCIS Search Result
    Interpolation Theorems for Nonmonotonic Reasoning Systems Dichotomy Theorems for Equalityfree Logic The Method of Diagrams and Preservation Theorems

    48. Wolter, Frank; Zakharyaschev, Michael: Intuitionistic Modal Logics
    On the interpolation property of some intuitionistic modal logics. of superintuitionistic logics syntax, semantics and preservation theorems.
    Category Value Available via Submitted on 4th of September 1998 Author Wolter, Frank; Zakharyaschev, Michael Title Intuitionistic Modal Logics Date of publication Published in To appear in Logic in Florence, 1995 Citation Wolter, Frank; Zakharyaschev, Michael. Intuitionistic Modal Logics, To appear in Logic in Florence, 1995 Number of pages Language English Organization The Institute of Computer Science Type Technical Report Subject group Computer Science, Data Processing Source(s)
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