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1. 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

Log in RSS Title Author(s) Abstract Subject Keyword All Fields FullText more options Home Browse Search ... next Barwise: infinitary logic and admissible sets H. Jerome Keisler and Julia F. Knight Source: Bull. Symbolic Logic Volume 10, Issue 1 (2004), 4-36. 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: http://projecteuclid.org/euclid.bsl/1080330272 Mathematical Reviews number (MathSciNet): Digital Object Identifier: doi:10.2178/bsl/1080330272 Zentralblatt Math identifier: back to Table of Contents previous next Bulletin of Symbolic Logic Current Issue All Issues Search this Journal Editorial Board ... Log in RSS Cornell University Library

2. JSTOR Infinitary Logic And Admissible Sets. Infinitary Logic and admissible sets. The journal of symbolic Logic, vol. 34 (1969), pp. 226252. It is regrettable that this paper, which opened new http://links.jstor.org/sici?sici=0022-4812(197103)36:1<156:ILAAS>2.0.CO;2-T

3. Logic And Computation Seminar At Penn Specifically we will introduce admissible sets and their connection to the Logic L_{omega_1, omega}. We will then review the model existence theorem and use http://www.cis.upenn.edu/~lc/seminar.html

Penn Logic and Computation Seminar 2007-2008 The Logic and Computation Group is composed of faculty and graduate students from the Computer and Information Science Mathematics , and Philosophy departments, and participates in the Institute for Research in the Cognitive Sciences . The Logic and Computation group runs a weekly seminar. The seminar is open to the public and all are welcome. The seminar meets regularly during the school year on Mondays at 4:30 p.m. in room DRL 4C8 on the fourth (top) floor of the David Rittenhouse Laboratory (DRL), on the Southeast corner of 33-rd and Walnut Streets at the University of Pennsylvania. Directions may be found here . Any changes to this venue or schedule will be specifically noted. Some upcoming talks: January 28: Dimitrios Vytiniotis, University of Pennsylvania Damien Pous Ecole normale superieure de Lyon and University of Pennsylvania December 10, 2007, 4:30 pm in DRL 4C8 Relation algebras, well-founded induction and commutation The calculus of relations has been introduced by Alfred Tarski, in an attempt to axiomatize the theory of binary relations, without dealing with individuals (the objects being related). It has also been called "relation algebras". Ten years ago, Doornbos, Backhouse and van der Woude [1997] showed that we can characterize the notion of a well-founded relation in a similar setting, so that we end up with the ability to reason by well-founded induction at this relatively high level of abstraction.

4. Bulletin Of Symbolic Logic, 2004; 10 (1) 1 Background on infinitary Logic /, 5. BARWISE INFINITARY Logic AND admissible sets 0 Introduction / Keisler, H Jerome / Knight, Julia F, 5 http://www.ucm.es/BUCM/compludoc/W/10404/10798986_1.htm

Sumario Título / Autor(es) Página(s) 1 Background on infinitary logic / BARWISE: INFINITARY LOGIC AND ADMISSIBLE SETS - Introduction / Keisler, H Jerome Knight, Julia F 1.1 Expressive power of Lw1w / 1.2 The back-and-forth construction / 1.3 The Scott isomorphism theorem / 1.4 w-logic / 1.5 Familiar theorems / 1.6 Failure of compactness / 2.1 D0 formulas and S-formulas in set theory / 2 Background on admissible sets / 2.2 Axioms of KP / 2.4 The admissible set L(wCK1) / 2.3 Examples of admissible sets / 3.1 Completeness and compactness / 3 Admissible fragments / 3.2 Computable structures via Barwise compactness / 3.3 Other applications of Barwise compactness / 4.1 KP with urelements / 4 Admissible sets over M / 4.2 Truncation lemma / 4.4 Inductive definitions / 4.3 Admissible sets above M / 5.1 Computable saturation / 5 Saturation properties / 5.2 SA-saturation / 6 Conclusion /

5. [math/0701788v1] Polish Group Actions And Admissible Sets Title Polish group actions and admissible sets. Authors B. MajcherIwanow Subjects, Logic (math.LO). MSC classes, 03E15 (Primary) 03C70 (Secondary) http://arxiv.org/abs/math.LO/0701788v1

arXiv.org math Search or Article-id Help Advanced search All papers Titles Authors Abstracts Full text Help pages Full-text links: Download: PostScript PDF Other formats Citations CiteBase p revious n ... ext Mathematics > Logic Title: Polish group actions and admissible sets Authors: B. Majcher-Iwanow (Submitted on 27 Jan 2007) Abstract: We generalize some model theory involving Hyp(M) and HF(M) to the case of actions of Polish groups on Polish spaces. In particular we obtain two variants of the Nadel's theorem about relationship between Scott sentences and admissible sets. Comments: 44 pages, AMSLaTeX Subjects: Logic (math.LO) MSC classes: 03E15 (Primary) 03C70 (Secondary) Cite as: arXiv:math/0701788v1 [math.LO] Submission history From: Barbara Majcher-Iwanow [ view email Sat, 27 Jan 2007 00:07:21 GMT (35kb) Which authors of this paper are endorsers? Link back to: arXiv form interface contact

6. Mathematical Logic And Theoretical Computer Science A.S.Morozov, On Sdefinability of admissible sets, In Proceedings of Logic Colloquium-98, Praha, 9-15 August, S. Buss, P. Hájek, P. Pudlák eds. p. 334-351. http://www.math.uni-heidelberg.de/logic/computability2001/abstracts.html

Workshop on COMPUTABILITY AND MODELS Heidelberg, Germany, January 18-20, 2001 Abstracts of Contributed Talks Marat Arslanov, Models of Relative Computability and the Ershov Hierarchy In second part of my talk I will consider general conditions under which relative splittings and specified diamond embeddings are derivable in the local structure of the enumeration degrees. General questions of definability and the role of splitting and nonsplitting, and also the description of new relationships between information content and degree theoretic structure will be considered. Serikzhan Badaev, Spectrum of Computable Minimal Numberings We consider computable minimal numberings of the families of arithmetical sets (see [1] for the necessary notions). Let A S n be any S n w w S n - computable minimal numberings of A . The triple (d,p,m) is called spectrum of computable minimal numberings of A The problem of description of the triples which realize spectrums of computable minimal numberings for the families in a given level of hierarchy arose from the long-standing problem of Yu.L.Ershov on possible number of computable minimal numberings of the families of c.e. sets. Note that not every triple could be a spectrum of some family of c.e. sets. This follows from the following theorem of S.S.Goncharov [2]: if a family of c.e. sets has decidable but not the least computable numbering under reducibility then it has w positive computable numberings.

7. Infinitary Logic - Wikipedia, The Free Encyclopedia An infinitary Logic is a Logic that allows infinitely long statements and/or infinitely long proofs. . Kenneth Jon Barwise, admissible sets. http://en.wikipedia.org/wiki/Infinitary_logic

var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia"; Infinitary logic From Wikipedia, the free encyclopedia Jump to: navigation search 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 A word on notation and the axiom of choice Definition of Hilbert-type infinitary logics Completeness, compactness and strong completeness

8. 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

9. Mhb03.htm 03C70, Logic on admissible sets. 03C75, Other infinitary Logic. 03C80, Logic with extra quantifiers and operators See also 03B42, 03B44, 03B45, 03B48 http://www.mi.imati.cnr.it/~alberto/mhb03.htm

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.)

10. Logic Colloquium 1997 - Contributed Papers Antonino Drago (Napoli) Vasiliev s Paraconsistent Logic Interpreted by . Cyrus F. Nourani (Project METAA1) Functorial Models, admissible sets and 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

11. MathNet-Mathematical Subject Classification 03C70, Logic on admissible sets. 03C75, Other infinitary Logic. 03C80, Logic with extra quantifiers and operators See also 03B45 http://basilo.kaist.ac.kr/API/?MIval=research_msc_1991_out&class=03-XX

12. The Journal Of Symbolic Logic, Volume 34 219225 BibTeX Jon Barwise Infinitary Logic and admissible sets. 226-252 BibTeX M. J. Cresswell A Conjunctive Normal Form For S3.5. http://www.informatik.uni-trier.de/~ley/db/journals/jsyml/jsyml34.html

The Journal of Symbolic Logic , Volume 34 Volume 34, Number 1, March 1969 Richmond H. Thomason D. Randolph Johnson Jr. : Predicate Calculus with Free Quantifier Variables. 1-7 BibTeX J. B. Florence : Partially Ordered Sets Representable by Recursively Enumerable Classes. 8-12 BibTeX Matthew J. Hassett : Recursive Equivalence Types and Groups. 13-20 BibTeX A. B. Slomson : An Undecidable Two Sorted Predicate Calculus. 21-23 BibTeX Pavel Materna : Identity, Equivalence and Isomorphism of Problems. 24-34 BibTeX David Makinson : A Normal Modal Calculus Between T and S4 Without the Finite Model Property. 35-38 BibTeX Louise Hay : Index Sets of Finite Classes of Recursively Enumerable Sets. 39-44 BibTeX Alfred B. Manaster : Rich Co-ordinals, Addition Isomorphisms, and Rets. 45-52 BibTeX Robert I. Soare : Sets with no Subset of Higher Degrees. 53-56 BibTeX Nino B. Cocchiarella : A Second Order Logic of Existence. 57-69 BibTeX Erik Ellentuck : A Choice Free Theory of Dedekind Cardinals. 70-84 BibTeX Manuel Lerman : Some Nondistributive Lattices as Initial Segments of the Degrees of Unsolvability. 85-98 BibTeX Yiannis N. Moschovakis

13. Lecture Notes In Logic - LNL 13 ASL Book Series Lecture notes in Logic and perspectives in Logic; ASL member Discounts; On $\Sigma$Definability of admissible sets. A. S. Morozov http://www.aslonline.org/books-lnl_13.html

Books Lecture Notes in Logic Perspectives in Logic Other ASL Books Member Discounts Available LNL volumes ... Editorial Board Lecture Notes in Logic, 13 Logic Colloquium '98 Proceedings of the Annual European Summer Meeting of the Association for Symbolic Logic, held in Prague, Czech Republic August 9-15, 1998 Sam Buss, Petr Hajek, Pavel Pudlak, editors This book is the proceedings of the 1998 European Summer Meeting of the Association for Symbolic Logic, Logic Colloquium '98. The meeting was held at the University of Economics in Prague, August 9-15, 1998. This volume contains papers covering current research from all areas of mathematical logic, including Proof Theory, Set Theory, Model Theory, Computability Theory, and Philosophy. There are twelve articles on Proof Theory; a survey of fuzzy logic; nine articles on Set Theory; four articles on H. Rogers' 1965 agenda for recursive function theory; four articles on Model Theory; and two articles on Belief Theories. A number of these articles deal with theoretical computer science. Year: 2000 Price:$85.00

14. Conferences , 10.1093/jigpal/jzm007 Logic Journal Of IGPL Logic Journal of IGPL Advance Access published online on May 15, 2007 . of recursive functions on admissible sets and schematic reflection principles. http://jigpal.oxfordjournals.org/cgi/content/full/jzm007v1?ck=nck

15. Yuri Leonidovich Ershov (on His 60th Birthday) S S Goncharov, I A 96, Dynamic Logic over admissible sets , Dokl. Akad. Nauk SSSR, 273 (1983), 1045–1048; English transl. Soviet Math. Dokl., 28 (1983), 739–742 http://www.turpion.org/php/reference.phtml?journal_id=rm&paper_id=354&volume=55&

16. No Title ``A guide to the identification of admissible sets above structures , Annals of Mathematical Logic 12, 1977, 151192. ``Ordinal Spectra of first order http://www.ececs.uc.edu/~schlipf/vita.forweb/index.html

Next: About this document Curriculum Vita: John S. Schlipf Professor, Computer Science, and Member of the Graduate Faculty College of Engineering The University of Cincinnati Cincinnati, OH 45221-0030, USA Employment History: 1983-Present: Professor of Computer Science (1993-Present) Associate Professor of Computer Science (1987-1993), Assistant Professor of Computer Science (1984-1987), and Assistant Professor of Mathematical Sciences (1983-1984), University of Cincinnati. Associate Head for Computer Science University of Cincinnati Spring 1995: Visiting Scholar, University of Kentucky Summer 1991: Visitor at Mathematical Sciences Institute, Cornell University. Senior Computer Specialist, Dynamac Corporation, Information and Management Systems Division. Part time instructor in computer science, St. Mary's College of Maryland. Assistant Professor of Mathematics, St. Mary's College of Maryland. Visiting Lecturer in Mathematics, University of Illinois, Urbana-Champaign. Bateman Research Instructor of Mathematics, California Institute of Technology. Education: Undergraduate, Carleton College, Northfield, Minnesota. B.A., 1970, mathematics, magna cum Laude.

17. Logic Colloquium 2003 Classical and nonclassical Logic, Hall 1, Friday 15.8. . positive set theory; 17.00-17.20 Vadim Puzarenko On some aspects of theory of admissible sets http://www.math.helsinki.fi/logic/LC2003/abstracts/csc.html

Main Awards Registration Accommodation ... ASL Contributed talks schedule of LC2003 Model theory, Hall 5, Friday 15.8. John Baldwin: Local homogeneity, benign sets and expansions of models Koichiro Ikeda: Stability of generic pseudoplanes Aleksander Ivanov: Asylkhan Khisamiev: On quasiresolvable models Krzysztof Majcher: Model theory 2, Hall 6, Friday 15.8. A word on infinite forcing Fredrik S. G Engström: Omitting types in expansions and related strong saturation properties On interpolation and Lindström's Theorem in abstract logic without negation Markus Junker: Martin Goldstern: The Galois connection between relations and automorphism Recursion theory and arithmetic, Hall 10, Friday 15.8. Anatoly Beltiukov: Polynomially decidable theories of polynomial constructive arithmetic with recurring induction Evan J. Griffiths: Characterising Algorithmic Randomness Gyesik Lee and Andreas Weiermann: Giacomo Lenzi and Erich Monteleone: Set theory, Hall 13, Friday 15.8. Forcing notions in inner models Natasha L. Dobrinen: A very weak distributive law and a related game in Boolean algebras Sy David Friedman: Alex Hellsten: Killing a weakly compact set Justin Moore: Some remarks on OCA and the size of the continuum Proof theory, constructivism and philosophy of mathematics, Hall 12, Friday 15.8.

18. Sachgebiete Der AMS-Klassifikation: 00-09 03C52 Properties of classes of models 03C55 Settheoretic model theory 03C70 Logic on admissible sets 03C75 Other infinitary Logic 03C80 Logic with 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

19. Program The theory and practice of automated reasoning in firstorder Logic (Manchester), 12.15-13.00 Principles of computability on admissible sets. http://www.sbras.ru/ws/ALC-9/program.html

The 9th Asian Logic Conference 16-19 August, 2005, Novosibirsk, Russia Preliminary Conference Program Plenary lectures August 16 August 17 August 18 August 19 Opening of the conference Moshe Vardi Buechi complementation: a forty-year saga (Houston) Yurii Ershov Model theory for multi valued fields (Novosibirsk) Joseph Miller The degrees of unsolvability of continuous functions (Bloomington) Hiroakira Ono Interpolation property and principle of variable separation in substructural logics (Nomi) Vladimir Rybakov Admissible inference rules in temporal linear logics based at integer numbers (Manchester) Xishun Zhao Complexity results on minimal unsatisfiable formulas (Guangzhou) Vladimir Kanovei On two inductive Borel irreducibility theorems (Moscow) Andrei Mantsivoda Semantic programming for semantic web (Irkutsk) Sanjay Jain , Kinber E. Negative data in learning languages (Singapore) Masahiko Sato A natural framework for checking proofs (Kyoto) Lev Beklemishev On limit existence principles in formal arithmetic (Utrecht) Su Gao Unitary group actions and classification problems (Beijing, Denton)

20. Logic Colloquium 2006 Barbara MajcherIwanow, Polish group actions and admissible sets Martin Goldstern, Applications of Mathematical Logic in Algebra the lattice of clones http://www.cs.ru.nl/lc2006/invited.html

main invited contributed registration how to get there Invited talks This page contains the schedule and abstracts of the tutorials, the plenary talks and the special sessions at the Logic Colloquium 2006 Schedule 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 ( jasper@cs.ru.nl ) who will have it pre-installed on the presentation computer. Room 1 Samson Abramsky, Categorical Quantum Logic Room 1 Ieke Moerdijk, Introduction to Algebraic Set Theory (First Part) Room 1 Marat Arslanov, Problems of definability and structural differences among elementary theories of the Ershov difference hierarchy Room 1 (Chair: Ralf Schindler) Natasha Dobrinen, Co-stationarity of the ground model, internal consistency, and new sequences John Krueger, Some Consistency Results Related to Internal Approachability Room 2 (Chair: Michael Rathjen) Klaus Aehlig

21. Infinitary Logic (Stanford Encyclopedia Of Philosophy/Spring 2004 Edition) Barwise, J., 1967, Infinitary Logic and admissible sets. Makkai, M., 1977, admissible sets and Infinitary Logic , Handbook of Mathematical Logic, http://www.science.uva.nl/~seop/archives/spr2004/entries/logic-infinitary/

This is a file in the archives of the Stanford Encyclopedia of Philosophy version history HOW TO CITE THIS ENTRY Stanford Encyclopedia of Philosophy A B C D ... Z This document uses XHTML-1/Unicode to format the display. Older browsers and/or operating systems may not display the formatting correctly. last substantive content change SEP Infinitary Logic sets makes it no longer necessary to regard formulas as inscriptions, and suggests the possibility of fashioning "languages" some of whose formulassuch as that in the above quotationwould be naturally identified as infinite sets . A "language" of this kind is called an infinitary language : in this article we 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 we shall see 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

22. The American Philosophical Association: News Announcement K. Jon Barwise Memoria His first book, admissible sets and Structures (1975), developed the theory of admissible sets, and applied it to definability theory, a branch of Logic http://www.apa.udel.edu/apa/news/01292002.html

Search Site Map Contact Us National Office News ... Paper Submissions Governance By-Laws Board of Officers Board Meeting Minutes Committees ... Permission Fees Profession Data APA Statements Average Faculty Salaries Advertising Advertising Advertising in JFP Resources Conferences, Seminars JobSeeker Database Teaching Committee's Online Resource Center ... Other Publications Member Services Membership Info Becoming a Member Members Only Section Login Member Section Index Services: Membership Directory Resources: Jobs for Philosophers APA Newsletters Member Home Pages Grants, Fellowships and Prizes ... Sabbatical Housing APA News Announcements K. Jon Barwise Memorial K. Jon Barwise was a world-renowned logician known for his research in mathematical logic, his ingenuity in applying mathematical techniques to outstanding problems in other disciplines, and his pioneering efforts in logic pedagogy. Jon Barwise received his B.A. in Mathematics and Philosophy from Yale University in 1963. He received a Ph.D. in Mathematics in 1967 from Stanford University, where he wrote his dissertation under Professor Solomon Feferman of Stanford. He also studied with Professor Dana Scott, now at Carnegie Mellon University, and Professor Georg Kreisel. In 1992 he was awarded an honorary doctorate from the University of Pennsylvania. Barwise was College Professor of Philosophy, Computer Science, and Mathematics at Indiana University. He joined the faculty at Indiana University in 1990. Between 1983 and 1990, he was a professor of philosophy at Stanford, where he was a co-founder and first director of the Center for the Study of Language and Information, and the first director of the Symbolic Systems Program.

23. The Logic Of Defeasible Argumentation Table of Contents. The Logic of defeasible argumentation Argument attack and argument defeat admissible sets and argumentation stages http://www.ai.rug.nl/~verheij/teaching/defarg/attack/

The logic of defeasible argumentation Click here to start Table of Contents The logic of defeasible argumentation Argument attack and argument defeat Overview Pollock’s undercutters and rebutters ... PPT Slide Author: Bart Verheij Email: b.verheij at ai dot rug dot nl Home Page: http://www.ai.rug.nl/~verheij/

24. List KWIC DDC22 510 And MSC+ZDM E-N Lexical Connection Logic of knowledge and belief 03B42 Logic of natural languages 03B65 Logic of vagueness fuzzy Logic; 03B52 Logic on admissible sets 03C70 http://www.math.unipd.it/~biblio/kwic/msc-cdd/dml2_11_33.htm

linear integral equations # systems of linear integral equations # systems of nonsingular linear integral equations # systems of singular linear logic and other substructural logics linear logic, Lambek calculus, BCK and BCI logics) # substructural logics (including relevance, entailment, linear mappings, matrices, determinants, theory of equation) # linear algebra. multilinear algebra. (vector spaces, linear models # generalized linear operators linear operators # equations and inequalities involving linear operators # equations with linear operators # general theory of linear operators # groups and semigroups of linear operators # special classes of linear operators (operator and matrix valued functions, etc., including analytic and meromorphic ones) # functions whose values are linear operators as elements of algebraic systems # individual linear operators) # linear relations (multivalued linear operators, their generalizations and applications # groups and semigroups of linear operators, with operator unknowns # equations involving

25. 03Cxx 03C52 Properties of classes of models; 03C55 Settheoretic model theory 03C70 Logic on admissible sets; 03C75 Other infinitary Logic; 03C80 Logic with 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.)

26. Alfred Tarski Centenary Conference Jaakko Hintikka, Independencefriendly Logic and axiomatic set theory Dexter Kozen, A Computer Scientist s View of admissible sets; Joachim Lambek, http://www.mimuw.edu.pl/TARSKI/tytuly.html

[Alloout d Back to main page Alfred Tarski Centenary Conference Tentative list of proposed talks Zofia Adamowicz , Consistency, incompleteness and non-conservativeness in arithmetic John W. Addison Jr. Tarski's theory of definability: common themes in descriptive set theory, recursive function theory, classical pure logic, and finite-universe logic. Paola D'Aquino , Around quadratic reciprocity law in weak fragments of Arithmetic Arnon Avron, Non-deterministic Matrices Arnold Beckmann Models and separations of bounded arithmetic Lev Beklemishev Provability algebras and proof-theoretic ordinals Arianna Betti Lesniewski's Early Solution to the Liar and Tarski Andreas Blass Some cardinal characteristics of the continuum Aleksander Blaszczyk Free Boolean Algebras and Nowhere Dense Ultrafilters Willem Blok , On equivalence of deductive systems Sam Buss , Extracting feasible algorithms from intuitionistic proofs Janusz Czelakowski , Abstract algebraic logic and hierarchies of deductive systems G. Cattaneo, M. L. Dalla Chiara, R. Giuntini An unsharp quantum logic from quantum computation Lou van den Dries

27. Publications Of V.N. Remeslennikov Weak Second Order Logic in Group Theory//‘ont.Math. Part 1. 1992, V.131. P.273278. (with Myasnikov A.G.); admissible sets in group theory//Algebra i logika http://www.univer.omsk.su/departs/math/cmathlog/staff/vnr/p-vnr.html

Publications of V.N.Remeslennikov Back to the personal home page the page of MLLP division About completions of groups //Doklady Akademii nauk SSSR. 134, 1960, p.518-520 (with M.I. Kargapolov, Y.I.Merzljakov) (Russian). About one method of completion groups //Research records of Perm Univ. 17. P.9-11. (with M.I. Kargapolov, Y.I. Merzljakov) (Russian). Two remarks of three step-nilpotent groups // Algebra i logika. V.4, N2, 1965. P.59-65. (Russian). Conjugacy in free decidable groups //Algebra i logika. V.5, N6, 1966. P.15-25. (with M.I. Kargapolov) (Russian). Conjugacy of subgroups in nilpotent groups //Algebra i logika, V.6,N2, 1967. P.61-76. (Russian). Residual finitness relative to conjugacy for interlacings // in Proc. of 8-th All-Union Colloquium on General Algebra. - Riga, 1967. (Russian). Foundations of group theory. P. 1. - Novosibirsk, 1968. 206 p. (with M.I. Kargapolov, Y.I. Merzljakov) (Russian). Residually finitness of metabelian groups // Algebra i logika. V.7, N4, 1968. P.106-113. (Russian). About residual finitness relative to conjugacy for free products // Novosibirsk, V.1. 1969. (Russian).

28. Sessione A. I. Stukachyov, Representations of models in admissible sets and syntactic V. F. Murzina, A modal Logic that is complete with respect to strictly http://math.nsc.ru/~alglog/ses2004e.html

Sessions of the Seminar "Algebra i Logika" 1387th session. Feb. 4, 2004. I. A. Mal'tsev, Transitive iterative algebras. 1388th session. Feb. 10, 2004. 1389th session. Feb. 17, 2004. V. V. Bludov (Irkutsk), Completion of linearly ordered groups. V. V. Bludov (Irkutsk), The variety of lattice-ordered groups approximable by linearly ordered groups. 1390th session. Feb. 24, 2004. Yu. L. Ershov, Extremal valued fields. 1391st session. March 3, 2004. A. T. Gainov, -orthograded quasi-monocomposition algebras with one-dimensional nil component. 1392nd session. March 9, 2004. D. G. Khramtsov, Endomorphisms of automorphism groups of free groups. 1393th session. March 16, 2004. S. S. Goncharov, V. S. Harizanov (Washington, USA), J. F. Knight (Notre Dame, USA), C. F. McCoy (Notre Dame, USA), R. Miller (New York, USA), and D. R. Solomon (Wisconsin, USA), Numberings in computable structure theory. 1394th session. March 23, 2004. 1395th session. March 30, 2004. S. A. Zyubin (Krasnoyarsk), Conjugate-dense subgroups in free products. 1396th session. April 13, 2004.

29. GCasp Graphs And Colorings For Answer Set Programming Now a sequence of operators 2,3 computes admissible colorings of the RDG which correspond to the answer sets of the Logic program. http://www.cs.uni-potsdam.de/~konczak/system/gcasp/

Wissensverarbeitung und Informationssysteme GCasp Graphs and colorings for answer set programming Kathrin Konczak and Thomas Linke and Torsten Schaub Contents Introduction Architecture Installation Getting started ... Bibliography Introduction We investigate rule dependency graphs and their colorings for characterizing the computation of answer sets of logic programs [ ]. To this end, we develop a series of operational characterizations in terms of operators on partial colorings. Our characterizations are expressed as (non-deterministically formed) sequences of colorings, turning an uncolored graph into a totally colored one. This results in an operational framework in which different combinations of operators result in different formal properties. The GCasp system is divided in several components which read a logic program out of a file, generate the rule dependence graph (RDG), which represents the logic program, and compute the admissible colorings , which corresponds to the answer sets of the logic program. The implementation is written for different Prolog systems like ECLiPSe SICStus and SWI . Additionally, the well-founded semantics [

30. Prague Vienna 2006 In classical Logic all admissible rules are also derivable, but in intuitionistic and many other nonclassical Logics this is not the case. sets of rules http://www.phil.uu.nl/~jjoosten/events/PragueVienna2006/

Prague-Vienna workshop on Proof Theory and Proof Complexity, 2006 Schedule Prague Vienna Workshop 2006 Wednesday 11-1-2006 Thursday 12-1-2006 10:00-10:40 Mathias Baaz 10:40-11:20 Joost J. Joosten 10:40-11:20 Arnold Beckmann 11:20-11:35 Tea and Coffee 11:20-11:35 Tea and Coffee 11:35-12:15 Markus Latte 11:35-12:15 Rosalie Iemhoff 12:15-14:00 Lunch 12:15-14:00 Lunch 14:00-14:40 Alan Skelley 14:40-15:20 Marta Bilkova 14:40-15:20 George Metcalfe 15:20-15:40 Tea and Coffee 15:20-15:40 Tea and Coffee 15:40-16:20 Vitezslav Svejdar 15:40-16:20 Evan Goris 16:20-17:00 Pavel Hrubes 16:20-17:00 Jan Krajicek COORDINATES are as follows. The workshop takes place at Zitna 25 on Wednesday January 11 and Thursday January 12. The conference room shall be indicated with signs to find it. If you are at Zitna 25, there is big door which looks like a little "archway". You can recognize this by the flowershop on the lefthand side. You go through the archway across the courtyard and the institute is through the glass doors at the end. To find your way around in Prague it is very good to use www.mapy.cz

31. Hyperlinked List Of Shelah's Papers: The 100's Sh100 Shelah, Independence results J Symbolic Logic 45 (1980) 563573 . Countably decomposable admissible sets Annals Pure and Applied Logic 26 http://shelah.logic.at/short100.html

Hyperlinked list of Shelah's papers: the 100's Prepared on 2007-07-07 This is only a partial list. The full list is elsewhere Sh:100 Shelah, Independence results J Symbolic Logic 45 (1980) 563-573 MwSh:101 Makowsky+Shelah, The theorems of Beth and Craig in abstract model theory. II. Compact logics Archiv fur Math Logik und Grundlagenforschung 21 (1981) 13-35 AbSh:102 Avraham (Abraham)+Shelah, Forcing with stable posets J Symbolic Logic 47 (1982) 37-42 FrSh:103 Fremlin+Shelah, On partitions of the real line Israel J Math 32 (1979) 299-304 LvSh:104 Sh:105 Shelah, On uncountable abelian groups Israel J Math 32 (1979) 311-330 AbSh:106 Sh:107 Shelah, Models with second order properties. IV. A general method and eliminating diamonds Annals Pure and Applied Logic 25 (1983) 183-212 Sh:108 Shelah, On successors of singular cardinals Logic Colloquium '78 (Mons, 1978) (1979) 357380 HoSh:109 Hodges+Shelah, Infinite games and reduced products Annals Math Logic 20 (1981) 77-108 Sh:110 Shelah, Better quasi-orders for uncountable cardinals Israel J Math 42 (1982) 177-226 Sh:111 Shelah, On power of singular cardinals Notre Dame J Formal Logic 27 (1986) 263-299

32. LC '77: Contributed Papers European Meeting of the Association for Symbolic Logic Set theory in model theory; Richard Mijoule admissible sets using L ; Stanley H. Stahl http://july2007.ii.uni.wroc.pl/lc77accepted.html

Logic Colloquium '77 European Meeting of the Association for Symbolic Logic Thirty years before LC 2007, LICS 2007, ICALP 2007, and PPDP 2007 Home Overview Invited lectures ... Satellite workshops Contributed papers On probability logic Mohamed A. Amer Cyclic indiscernibles Dionysis A. Anapolitanos Dimension-restricted free cyclic algebras and finitary logic of infinitary relations H. Andr©ka, T. Gergely and I. N©meti Toward a unified treatment of certain algebraic logics H. Andr©ka, T. Gergely and I. N©meti Injective Hull = algebraic closure Paul D. Bascsich The infinite fine spectrum of universal Horn theories John T. Baldwin The theory of Abelian p -groups with the unifier I is decidable Andreas Baudisch Rigid Boolean algebras Robert Bonnet Remark on Yu. Gurevich's paper on “The decision problem for standard classes” Egon B¶rger Semantics of intuitionistic connectives Kenneth A. Bowen Effective coloration of countable graphs of finite genus Hans Georg Carstens Monoids of normal forms Mario Coppo and Mariangiola Dezani-Ciancaglini Can syntax be ignored during translation?

33. PhD J. Barwise admissible sets and structures. M. Manzano Higher order Logic (in preparation). - I. Sain There are general rules for specifying semantics. http://phil.elte.hu/logic/english/phd.html

Logic Postgraduate School Budapest CURRICULUM I. General outline II. List of course titles Introductory (preliminary) courses Introduction to Universal Algebra Classical Extensional Logic Central courses: Classical Logic Set Theory Modal Logic Model Theory Algebraic Logic Metalogic Intensional logic Logic and Natural Language, Formal Semantics Further recommended courses: Logics of programs Tarski and Trends in 20th Century Philosophical Logic (History of Logic) Chapters from Philosophical Logic (cf. Handbook of Phil. Log.) Temporal logic and related subjects Boolean Algebras with Operators (connections with Kripke style semantics for nonclassical logics) History of Logic L-IV. Philosophy of foundations of mathematics, main direction Peano Arithmetic Artifacts in logic Logic and Cosmology Theories of Partial Semantics Category Theoretic Approaches to Algebraic Logic Category theory (introduction, foundations, connections with varieties, quasivarieties, free algebras etc.) III. Course descriptions

34. [PVS] Computability In Europe 2006 - Call For Participation Andrews) LJQ a focused calculus for intuitionistic Logic Thomas Ehrhard . of Reals in admissible sets Rose Hafsah Abdul Rauf (Swansea) Integrating http://pvs.csl.sri.com/mail-archive/pvs/msg02783.html

Date Prev Date Next Thread Prev Thread Next ... Thread Index [PVS] Computability in Europe 2006 - Call for Participation To pvs@csl.sri.com Subject : [PVS] Computability in Europe 2006 - Call for Participation From A.Beckmann@swansea.ac.uk (Arnold Beckmann) Date : Fri, 21 Apr 2006 08:18:14 +0100 List-Archive http://lists.csl.sri.com/mailman/private/pvs List-Help mailto:pvs-request@csl.sri.com?subject=help List-Id List-Post mailto:pvs@csl.sri.com List-Subscribe http://lists.csl.sri.com/mailman/listinfo/pvs mailto:pvs-request@csl.sri.com?subject=subscribe List-Unsubscribe http://lists.csl.sri.com/mailman/listinfo/pvs mailto:pvs-request@csl.sri.com?subject=unsubscribe Sender pvs-bounces+archive=csl.sri.com@csl.sri.com User-Agent : nail 11.4 8/29/04 [Apologies for multiple copies] CiE 2006 Computability in Europe 2006 : Logical Approaches to Computational Barriers 30 June - 5 July 2006 Swansea University, United Kingdom http://www.cs.swansea.ac.uk/cie06/ cie06@swansea.ac.uk CALL FOR PARTICIPATION Important deadlines: Informal Presentations 30 April, 2006 Early registration 15 May, 2006 * Some grants for UK students are still available * CiE 2006 is the second of a new conference series which serves as an interdisciplinary forum for researchers into all aspects of computability and the foundations of computer science. The scientific programme consists of two three-hour tutorials, nine plenary talks, six special sessions with four talks each, and over sixty contributed talks. For more details on the programme see the full list of talks below, or visit

35. Logic In Informatics : Mykola (Nikolaj) Stepanovich Nikitchenko In the third case we construct a special Logic of hierarchical nominative data in the style of KripkePlatek theory of admissible sets. http://www.management.kiev.ua/logic/people/msn.html

Go to Logic in Informatics Home Page Mykola (Nikolaj) Stepanovich Nikitchenko Prof. Dr. Mykola (Nikolaj) Stepanovich Nikitchenko Chairman of the Department of Theory of Programming of the Faculty of Cybernetics at the National Taras Shevchenko University of Kyiv. See below: Short C.V. Membership, Positions, Participation in Projects Scientific Interests Main Publications ... Photos SHORT CURRICULUM VITAE Born: 1951, Berdichev, Ukraine Student: Kiev Taras Shevchenko State University, Faculty of Mechanics and Mathematics (1968 – 1969), Faculty of Cybernetics (1969 - 1973) Candidate of physics and mathematics (Ph.D) and Doctor of physics and mathematics by speciality “Mathematical and program software of computers and systems” Employment: Kiev State University, Faculty of Cybernetics, Department of Programming Theory: since 1973 on positions of Assistant Professor, Lecturer, Associate Professor. Now Professor, Chairman of the department. Miscellaneous: Improvement in skill: Institute of Cybernetics (Kiev, 1976), Novosibirsk State University (Novosibirsk, 1982)

36. Upcoming Conferences | Doctoral Program In Computer Science 0803-01 Logic and the Foundations of Game and Decision Theory (2008) Greece Urlhttp//www.cs.swan.ac.uk/cie08/ Keywords admissible sets Algorithms http://146.96.245.153/news/conferences

@import "/files/css/2597047487d9c0e0d4a278c2d2595805.css"; @import "/themes/rose/print.css"; Login Search Links Location ... Links Upcoming Conferences 08-03-28 VII Jornadas de Ingenier­a Telem¡tica (2008) Thu, 12/20/2007 - 14:22 VII Jornadas de Ingenier­a Telem¡tica (Jitel2008-08) Date:Sep 16 08 to Sep 18 08 Deadline:Mar 28 08 Location:Alcal¡ de Henares, Spain Url: http://www.jitel.org/ Categories: Upcoming Conferences 08-01-25 Optimisation in Multi-Agent Systems (2008) Thu, 12/20/2007 - 11:27 Optimisation in Multi-Agent Systems (OptMAS-08) Date:May 12 08 Deadline:Jan 25 08 Location:Estoril, Portugal Url: http://www.optmas08.org/ Categories: Upcoming Conferences 08-01-25 Workshop on Agent-based Complex Automated Negotiation (2008) Thu, 12/20/2007 - 11:22 Workshop on Agent-based Complex Automated Negotiation (ACAN-08) Date:May 12 08 Deadline:Jan 25 08 Location:Estoril, Portugal Url: http://www-itolab.mta.nitech.ac.jp/ACAN2008/ Categories: Upcoming Conferences 08-03-24 Twelfth International Workshop on Cooperative Information Agents (2008) Thu, 12/20/2007 - 11:12 Twelfth International Workshop on Cooperative Information Agents (CIA-08) Date:Sep 10 08 to Sep 12 08 Deadline:Mar 24 08 Location:Prague, Czech Republic Url:

37. Literatura Jon Barwise, (editor) Handbook of Mathematical Logic, NorthHolland, Amsterdam, 1974. Jon Barwise, admissible sets and Structures, Springer-Verlag, http://aragorn.pb.bialystok.pl/~radev/literat.htm

Literatura A B C D ... Z A Peter Aczel Non Well-Founded Sets , CSLI, Stanford, 1988 A. Aho and J. Ullman The Theory of Parsing, Translation and Computing , Prentice-Hall, Englewood Cliffs, N.J, 1972. Robert Aumann and Sergiu Hort (editors) Handbook of Game Theory with Economic Applications vol. 1 , Elsevier, Amsterdam, 1992. Robert Aumann and Sergiu Hort (editors) Handbook of Game Theory with Economic Applications vol. 2 , Elsevier, Amsterdam, 1994. Allen, James. Natural language understanding. 2nd ed. Redwood City, Cal.: Benjamin/Cummings, 1995. B H. Barendregt The Lambda Calculus: Its Syntax and Semantics , North Holland, Amsterdam, 1984. H. Barendregt Functional programming and lambda calculus. , In Handbook of Theoretical Computer Science Jon Barwise, (editor) Handbook of Mathematical Logic , North-Holland, Amsterdam, 1974. Jon Barwise, Admissible Sets and Structures , Springer-Verlag, New York, 1975. M. Ben-Ari, Podstawy programowania wspó³bie¿nego i rozproszonego Johan van Benthem, Games in Logic, in J. Hoepelman, ed., Representation and Reasoning , Niemeyer Verlag, Tübingen, 3­-15, 165­-168, 1988 Johan van Benthem, Computation versus Play as a Paradigm for Cognition, Symposium for Jaakko Hintikka, Acta Philosophica Fennica 49, 236-­251. ,1990

38. InformIT: Frequently Asked Questions About Type-2 Fuzzy Logic And Fuzzy Sets > F Frequently Asked Questions About Type2 Fuzzy Logic and Fuzzy sets . It sits only on the permissible (sometimes called admissible ) values of x and w. http://www.informit.com/articles/article.aspx?p=21311

39. Mathematics Topics to be chosen from model theory and its applications, infinitary Logic and admissible sets, ordinary and generalized recursion theory, consistency and http://pr.caltech.edu/catalog/05_06/courses/listing/ma.html

The online version of the Caltech Catalog is provided as a convenience; however, the printed version is the only authoritative source of information about course offerings, option requirements, graduation requirements, and other important topics. Mathematics Ma 1 abc. Calculus of One and Several Variables and Linear Algebra. 9 units (4-0-5); first, second, third terms. Prerequisites: high-school algebra, trigonometry, and calculus. Special section of Ma 1 a, 12 units (5-0-7). Review of calculus. Complex numbers, Taylor polyno-mials, infinite series. Comprehensive presentation of linear algebra. Deriva-tives of vector functions, multiple integrals, line and path integrals, theorems of Green and Stokes. Ma 1 b, c is divided into two tracks: analytic and practical. Students will be given information helping them to choose a track at the end of the fall term. There will be a special section or sections of Ma 1 a for those students who, because of their background, require more calculus than is provided in the regular Ma 1 a sequence. These students will not learn series in Ma 1 a and will be required to take Ma 1 d. Instructors: Simon, Aschbacher, Wales, Ramakrishnan, Dunfield. Ma 1 d. Series.

40. SELECTED LOGIC PAPERS The author selects 23 of his papers in mathematical Logic that pursue Metarecursive sets (with G Kreisel); Post s Problem, admissible Ordinals, http://www.worldscibooks.com/mathematics/3598.html

Home Browse by Subject Bestsellers New Titles ... Browse all Subjects Search Bookshop New Titles Editor's Choice Bestsellers Book Series ... World Scientific Series in 20th Century Mathematics - Vol. 6 SELECTED LOGIC PAPERS by Gerald E Sacks The author selects 23 of his papers in mathematical logic that pursue definability via priority, forcing, compactness and fine structure applied to classical recursion, hyperarithmetic sets, recursion in objects of finite type, measure, models and E-recursion. His general introduction provides a chronology both personal and technical. Contents: On the Degrees Less Than 0' Recursive Enumerability and the Jump Operator The Recursively Enumerable Degrees are Dense A Simple Set Which is Not Effectively Simple Metarecursive Sets (with G Kreisel Post's Problem, Admissible Ordinals, and Regularity On a Theorem of Lachlan and Martin A Minimal Hyperdegree (with R O Gandy Measure-Theoretic Uniformity in Recursion Theory and Set Theory Recursion in Objects of Finite Type Forcing with Perfect Closed Sets The a -Finite Injury Method (with S G Simpson The 1-Section of a Type n Object Remarks Against Foundational Activity Countable Admissible Ordinals and Hyperdegrees The k -Section of a Type n Object Effective Bounds on Morley Rank Post's Problem, Absoluteness and Recursion in Finite Types

41. Infinitary Logic > Definition Of The Concept Of Admissible Set (Stanford Encyclo It is quite easy to see that if A is a transitive set such that A, A is a model of ZFC, then A is admissible. More generally, the result continues to http://plato.stanford.edu/entries/logic-infinitary/supplement.html

Cite this entry Search the SEP Advanced Search Tools ... Stanford University Supplement to Infinitary Logic Definition of the Concept of Admissible Set A nonempty transitive set A is said to be admissible when the following conditions are satisfied: (i) if a, b A a, b A and A A (ii) if a A and X A on A , then X a A (iii) if a A X A on A x a y x,y X ), then, for some b A x a y b x,y X separation scheme replacement scheme It is quite easy to see that if A A A ZFC , then A is admissible. More generally, the result continues to hold when the power set axiom is omitted from ZFC , so that both H H ) are admissible. However, since the latter is uncountable, the Barwise compactness theorem fails to apply to it. by John L. Bell jbell uwo ca

42. List Of Publications Of Sy David Friedman HC of an admissible Set, Journal of Symbolic Logic , Vol. 44, No. 1, March 1979, pp. 95102. Steel Forcing and Barwise Compactness, Annals of Mathematical http://www.logic.univie.ac.at/~sdf/papers/

List of Publications of Sy David Friedman (with Gerald Sacks Inadmissible Recursion Theory Bulletin AMS , Vol. 83, No. 2, 1977, pp. 255-256. An Introduction to Beta-Recursion Theory , in Generalized Recursion Theory II. Fenstad, Gandy, Sacks, eds., North-Holland, 1978, pp. 111-126. Beta-Recursion Theory Transactions AMS , Volume 255, 1979, pp. 173-200. Post's Problem Without Admissibility Advances in Mathematics , Vol. 35, No. 1, 1980, pp. 30-49. Negative Solutions to Post's Problem I GRT II , North Holland, 1978, pp. 127-133. Negative Solutions to Post's Problem II Annals of Mathematics , Vol. 113, 1981, pp. 25-43. Natural Alpha-RE Degrees, Logic Year 1979-1980 , University of Connecticut, Springer Lecture Notes 859 , 1981, pp. 63-66. The Turing Degrees and the Metadegrees Have Isomorphic Cones Patras Logic Symposiom , Metakides, Editor, North Holland, 1982, pp. 145-157. Some Recent Developments in Higher Recursion Theory Journal of Symbolic Logic , Vol. 48, No. 3, 1983, pp. 629-642. (with C.T. Chong) Degree Theory on Aleph-omega Annals of Pure and Applied Logic , Vol. 24, 1983, pp. 87-97.

43. Logic Programming For Modeling Social Choice A Logic programming for social choice problems with analysis of majority vote which seeks the sup of the size of admissible set of rankings satisfying http://www.us.kanto-gakuen.ac.jp/indo/wp/mplsc.html

Logic programming for modeling social choice updated: 22 Nov 2007 Tool box for social choice logic programming A collection of Prolog programs, which are applied to orderings and domain, social decision rules with their possibility theorems, domain conditions, and simple games. PROLOG Codes the automated proofs of the (im)possibility theorems: Arrow(1963), Gibbard-Satterthwaite(1973,1975), Wilson(1972), and Sen(1982). The following codes are cumulatively used. preference generator ( , revised 26 Dec 2006, 7 Jan 2007; 30 Oct 2007) Errata revision of cswf06.pl ( , revised 29 Oct 2007) I'm sorry for that I had mistakenly modeled IIA condition and other conditions. In the previous code these axioms are too loose so as to it could not constraint on the SWF patterns to derive only the dictatorial ones other than linear orderings. automated proofs for the Arrow's SWF and its variants ( , revised 24 Dec 2006, 5 Jul 2007) automated proofs for the Gibbard-Satterthwaite's SCF ( , revised 26 Dec 2006) common admissible domain and decomposability (Kalai-Muller theorem) ( , revised 6 Jan 2007) common (or individual) admissible domains: single-peakedness, value restriction, cyclical dependence and so on. (

44. WoLLIC'2006 - Content The latter replaces analogue formulations in terms of recursive functions on admissible sets and schematic reflection principles. http://www.cin.ufpe.br/~wollic/wollic2006/content.html

Content Title and Abstracts of Tutorial Lectures New insights into Probabilistically Checkable Proofs (PCPs) by Eli Ben-Sasson (Comput Sci Dept, Technion Inst of Technology, Israel) We revisit the celebrated PCP Theorem in light of recent simplifications to its proof and discuss new applications to error correcting codes and sub-linear time proof verification. Reminder : The celebrated PCP Theorem was proved in the early 1990's [Arora,Safra;Arora,Lund,Motwani,Sudan,Szegedy]. Informally speaking, it says there is a format of writing proofs and a probabilistic method of verifying their correctness. In this method the verifier needs to read only a constant number of random bits from the proof (independent of the proof length) to test its validity. Good proofs of true statements are accepted with probability one, whereas any purported "proof" of a false statement is rejected with probability of at least one third. Operational Theories of Sets by Solomon Feferman (Depts of Mathematics and Philosophy, Stanford University, USA)

45. Research An ordinal analysis of admissible set theory using recursion on ordinal notations Journal of Mathematical Logic, 291112, 2002 Abstract html, Paper dvi, http://www.andrew.cmu.edu/user/avigad/papers.html

Publications This list includes resarch articles, surveys, expository articles, unpublished notes, and a translation. I am also involved in a project to formalize parts of number theory in Isabelle . In 2004, we verified a proof of the prime number theorem; complete proof scripts are available on the project page. Local stability of ergodic averages with Philipp Gerhardy and Henry Towsner, submitted. Paper: arXiv Response to questionnaire to appear in Vincent F. Hendricks and Hannes Leitgeb, editors, Philosophy of Mathematics: 5 questions Book site: html , Paper: pdf (letter) pdf (a4) A decision procedure for linear "big O" equations with Kevin Donnelly, Journal of Automated Reasoning Abstract: html , Paper: journal arXiv , Implementation: sml A variant of the double-negation translation Carnegie Mellon Technical Report CMU-PHIL 179 Abstract: html , Paper: pdf (letter) pdf (a4) a lecture delivered at the ASL 2006 spring meeting in Montreal Paper: pdf (letter) pdf (a4) Understanding proofs to appear in Paolo Mancosu, editor

46. PHILOG - The Logic Of Time And Modality - Abstracts wellknown from classical propositional Logic, where the admissible This leads to a further representation of branching time simply as a set (of http://www.philog.ruc.dk/phiconf3abs.html

CONFERENCE ABSTRACTS Blackburn Copeland Fine Galton ... Simons PHILOG Wansing P Zanardo P Patrick Blackburn Title: An Introduction to Contemporary Hybrid Logic Abstract: In orthodox modal logic it is not possible to refer to the states (times, worlds, individuals...) of our models. This shortcoming renders modal logic unsuitable for many applications. Hybrid logic is a form of modal logic in which reference to states is possible; the key ideas trace back to work by Arthur Prior in the 1960s. Hybridisation not only improves the utility of modal logic, it also improves its metalogical properties in a number of ways; for example, general completeness and interpolation results can be proved, and a number of standard proof techniques (including natural deduction, sequent calculus, and resolution) can be straightforwardly adapted to hybrid logics. This is the first of two talks on hybrid logic. Here I present an overview of contemporary hybrid logic, stressing the intuitions which have guided its development, indicating the uses to which it can be put, and generally trying to make it clear exactly what advantages hybrid logic has over orthodox modal systems. I make little or no direct contact with the work of Arthur Prior; rather, my aim is to present a vivid snapshot of what contemporary hybrid logic is all about, and how it relates to current work in modal and description logic. I discuss Prior's work in my second talk.