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1. HeiDOK 03D60 Computability and recursion theory on ordinals, admissible sets, etc. ( 0 Dok. ) 03D65 Highertype and set recursion theory ( 0 Dok. http://archiv.ub.uni-heidelberg.de/volltextserver/msc_ebene3.php?zahl=03D&anzahl

2. Mhb03.htm 03D65, Highertype and set recursion theory. 03D70, Inductive definability. 03D75, Abstract and axiomatic computability and recursion theory 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.)

3. MathNet-Mathematical Subject Classification 03D60, recursion theory on ordinals, admissible sets, etc. 03D65, Highertype and set recursion theory. 03D70, Inductive definability http://basilo.kaist.ac.kr/API/?MIval=research_msc_1991_out&class=03-XX

4. Sachgebiete Der AMS-Klassifikation: 00-09 03D65 Highertype and set recursion theory 03D70 Inductive definability 03D75 Abstract and axiomatic recursion theory 03D80 Applications of recursion theory 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

5. DC MetaData For:The Hausdorff-Ershov Hierarchy In Euclidean Spaces 03D65 Highertype and set recursion theory 03D80 Applications of computability and recursion theory 03D55 Hierarchies 03E15 Descriptive set theory 03F60 http://www.math-inf.uni-greifswald.de/preprints/shadow/hemmerling03_25.rdf.html

computable analysis Hausdorff's difference hierarchy Ershov's hierarchy topological arithmetical hierarchy resolvable sets global and local depth of sets recursivity in analysis approximate decidability The Hausdorff-Ershov Hierarchy in Euclidean Spaces Armin Hemmerling Hemmerling Armin Preprintreihe Mathematik 2003, 25 The Hausdorff-Ershov Hierarchy in Euclidean Spaces Armin Hemmerling Preprint series: Preprintreihe Mathematik 2003, 25 MSC 2000 03D65 Higher-type and set recursion theory 03D80 Applications of computability and recursion theory 03D55 Hierarchies 03E15 Descriptive set theory 03F60 Constructive and recursive analysis 26E40 Constructive real analysis 68Q01 General Abstract This document is well-formed XML.

6. MSC 2000 : CC = Set 03D65 Highertype and set recursion theory; 03Exx set theory; 03E04 Ordered sets and their cofinalities; pcf theory Nouveau code MSC 2000 http://portail.mathdoc.fr/cgi-bin/msc2000.py?L=fr&T=Q&C=msc2000&CC=Set

7. List For KWIC List Of CCS 1998 And MSC2000 Phrases set functions, measures and integrals with values in ordered spaces 28B15 set interpretation instruction B.1.5.c set recursion theory Highertype and http://www.math.unipd.it/~biblio/kwic/msc-acm/cm-kl_11_51.htm

series of trigonometric and other functions; Riesz products # lacunary series resummation, etc.) # numerical methods (Monte_Carlo, series resummation, etc.) # numerical methods (Monte_Carlo, series rings # formal power series rings # power series solutions, expansion theorems series) # power series (including lacunary series) # series expansions (e.g. Taylor, Lidstone series, but not Fourier series, $_pF_q$ # generalized hypergeometric series, and generalizations # derived series, central series, auto-correlation, regression, etc. # time series, but not Fourier series) # series expansions (e.g. Taylor, Lidstone series, central series, and generalizations # derived series, etc.) # analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) # analytic approximation solutions (perturbation methods, asymptotic methods, series, etc.) # approximation to limiting values (summation of series, over-convergence # boundary behavior of power series, periods of modular forms, cohomology, modular symbols # special values of automorphic $L$- series, series of functions # power

8. 03Dxx 03D65 Highertype and set recursion theory; 03D70 Inductive definability; 03D75 Abstract and axiomatic recursion theory; 03D80 Applications of recursion http://www.ma.hw.ac.uk/~chris/MR/03Dxx.html

03Dxx Recursion theory 03D03 Thue and Post systems, etc. 03D20 Recursive functions and relations, subrecursive hierarchies 03D25 Recursively enumerable sets and degrees 03D30 Other degrees; reducibilities 03D35 Undecidability and degrees of sets of sentences 03D50 Recursive equivalence types of sets and structures, isols 03D55 Hierarchies 03D60 Recursion theory on ordinals, admissible sets, etc. 03D65 Higher-type and set recursion theory 03D70 Inductive definability 03D75 Abstract and axiomatic recursion theory 03D80 Applications of recursion theory 03D99 None of the above but in this section Top level of Index Top level of this Section

9. Theodore A. Slaman: Bibliography 03D65 Highertype and set recursion theory; 03D80 Applications of computability and recursion theory; 03Dxx Computability and recursion theory http://math.berkeley.edu/~slaman/papers/Publications_MSC.html

Theodore A. Slaman Home Bibliography Lectures Courses ... Links Bibliography Bibliography sorted by Mathematical Subject Classification Alternate Views Full Bibliography Bibserver Foundations of classical theories (including reverse mathematics) Effective and recursion-theoretic model theory Models of arithmetic and set theory Logic on admissible sets Complexity of computation Recursive functions and relations, subrecursive hierarchies Recursively (computably) enumerable sets and degrees Other Turing degree structures Other degrees and reducibilities Undecidability and degrees of sets of sentences Theory of numerations, effectively presented structures Recursive equivalence types of sets and structures, isols Hierarchies Computability and recursion theory on ordinals, admissible sets, etc. Higher-type and set recursion theory Applications of computability and recursion theory Computability and recursion theory Descriptive set theory Consistency and independence results Other aspects of forcing and Boolean-valued models Inner models, including constructibility, ordinal definability, and core models

10. MSC 2000 : CC = 03D 03D65 Highertype and set recursion theory; 03D70 Inductive definability; 03D75 Abstract and axiomatic computability and recursion theory http://math-doc.ujf-grenoble.fr/cgi-bin/msc2000.py?CC=03D&L=fr&C=msc2000&T=N

11. 03Dxx 03D65 Highertype and set recursion theory 03D70 Inductive definability 03D75 Abstract and axiomatic computability and recursion theory 03D80 Applications http://www.univie.ac.at/EMIS/MSC2000/03Dxx.html

Computability and recursion theory 03D03 Thue and Post systems, etc. 03D05 Automata and formal grammars in connection with logical questions [See also ] 03D10 Turing machines and related notions [See also ] 03D15 Complexity of computation [See also ] 03D20 Recursive functions and relations, subrecursive hierarchies 03D25 Recursively (computably) enumerable sets and degrees 03D28 Other Turing degree structures 03D30 Other degrees and reducibilities 03D35 Undecidability and degrees of sets of sentences 03D40 Word problems, etc. [See also ] 03D45 Theory of numerations, effectively presented structures [See also ; for intuitionistic and similar approaches see ] 03D50 Recursive equivalence types of sets and structures, isols 03D55 Hierarchies 03D60 Computability and recursion theory on ordinals, admissible sets, etc. 03D65 Higher-type and set recursion theory 03D70 Inductive definability 03D75 Abstract and axiomatic computability and recursion theory 03D80 Applications of computability and recursion theory 03D99 None of the above, but in this section Version of December 15, 1998

12. PlanetMath: 03D60, , Computability and recursion theory on ordinals, admissible sets, etc. 03D65, -, Higher-type and set recursion theory http://planetmath.org/browse/categories/03Dxx/

(more info) Math for the people, by the people. Encyclopedia Requests Forums Docs ... RSS Login create new user name: pass: forget your password? Main Menu sections Encyclop¦dia Papers Books Expositions meta Requests Orphanage Unclass'd Unproven ... Classification talkback Polls Forums Feedback Bug Reports downloads Snapshots PM Book information News Docs Wiki ChangeLog ... About Browsing MSC leaves only (Case insensitive substrings, use '-' to exclude) 03Dxx - Computability and recursion theory Thue and Post systems, etc. Automata and formal grammars in connection with logical questions Turing machines and related notions Complexity of computation Recursive functions and relations, subrecursive hierarchies Recursively (computably) enumerable sets and degrees Other Turing degree structures Other degrees and reducibilities Undecidability and degrees of sets of sentences Word problems, etc. Theory of numerations, effectively presented structures Recursive equivalence types of sets and structures, isols Hierarchies Computability and recursion theory on ordinals, admissible sets, etc. Higher-type and set recursion theory Inductive definability Abstract and axiomatic computability and recursion theory Applications of computability and recursion theory Miscellaneous up top

13. Browse MSC2000 Computability and recursion theory on ordinals, admissible sets, etc. related 03D65. Highertype and set recursion theory, related http://www.zblmath.fiz-karlsruhe.de/MATH/msc/zbl/msc/2000/03-XX/03Dxx/dir

Contact Search Browse Instructions ... Main Changes 75th anniversary Zentralblatt MATH Home Facts and Figures Partners and Projects Subscription Service Database Gateway Database Mirrors Reviewer Service Classification ... Serials and Journals database Miscellanea Links to the Mathematical World Display Text version Printer friendly page Internal Browse MSC2000 - by section and classification TOP MSC2000 - Mathematics Subject Classification Scheme 03-XX Mathematical logic and foundations Computability and recursion theory Classification Topic X-ref Thue and Post systems, etc. related... Automata and formal grammars in connection with logical questions [See also related... Turing machines and related notions [See also related... Complexity of computation [See also related... Recursive functions and relations, subrecursive hierarchies related... Recursively computably enumerable sets and degrees related...

14. MSC 2000 : CC = Recursion 03D65 Highertype and set recursion theory; 03D75 Abstract and axiomatic computability and recursion theory; 03D80 Applications of computability and http://www.mathdoc.emath.fr/cgi-bin/msc2000.py?L=en&T=Q&C=msc2000&CC=Recursion

15. Zentralblatt MATH - MSC 2000 - Search And Browse 03D60 Computability and recursion theory on ordinals, admissible sets, etc. ZMATH. 03D65 Highertype and set recursion theory ZMATH http://www.zentralblatt-math.org/msc/search/?pa=03Dxx

16. 359/369 (Total 5522) NO 152 03E04 Ordered Sets And Translate this page 147, 03D75, Abstract and axiomatic computability and recursion theory. 146, 03D70, Inductive definability. 145, 03D65, Higher-type and set recursion theory http://www.mathnet.or.kr/mathnet/msc_list.php?mode=list&ftype=&fstr=&page=359

17. General General Mathematics Mathematics For Nonmathematicians Highertype and set recursion theory Inductive definability Abstract and axiomatic computability and recursion theory Applications of computability and http://amf.openlib.org/2001/msc2000.xsd

18. Nabble - Coq - CiE08 - 2nd Call For Papers Higher type recursion theory and applications (organized by U. Berger, Swansea, and D. Effective descriptive set theory * Finite model theory http://www.nabble.com/CiE08---2nd-Call-for-Papers-td13833817.html

Nabble.setVar("skin",null); Nabble.page = 'forum.TopicDump'; Nabble.addCssRule(document.styleSheets[0],'.nabble a:link','color:'+document.linkColor); Nabble.addCssRule(document.styleSheets[0],'.nabble a:visited','color:'+document.vlinkColor); Nabble Math Mathematical Logics Coq Nabble.userHeader(2323); CiE08 - 2nd Call for Papers View: Threaded Chronologically All Messages Nabble.selectOption(Nabble.get("nabble.viewSelect"),Nabble.tview); New views Rating Filter: Alert me CiE08 - 2nd Call for Papers document.write(Nabble.ratingStars(3)); by document.write(''); Arnold Beckmann document.write(''); document.write(Nabble.formatDateLong(new Date(1195459494000))); :: Rate this Message: Reply to Author View Threaded Show Only this Message [Apologies for multiple copies] SECOND CALL FOR PAPERS CiE 2008 http://www.cs.swan.ac.uk/cie08/ Computability in Europe 2008: Logic and Theory of Algorithms University of Athens Athens, June 15-20 2008 PAPER SUBMISSION is now OPEN: http://www.cs.swan.ac.uk/cie08/submission.php

19. [Nyaya] Computability In Europe: Call For Papers Seisenberger, Swansea) Higher type recursion theory and applications (organized models * Effective descriptive set theory * Finite model theory * Formal http://www.cmi.ac.in/pipermail/nyaya/2007-November/000000.html

[Nyaya] Computability in Europe: Call for Papers ALI ali at cmi.ac.in Tue Nov 20 00:36:13 IST 2007 Next message: [Nyaya] Forwarded announcement from Joe Halpern Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Hi, I append the call for papers for Computability in Europe 2008 below. Please forward it to others you know who might be interested. Cheers, Suresh S P Suresh Chennai Mathematical Institute - Subject: CiE08 - Call for Papers [Apologies for multiple copies] ****************************************************************** CiE 2008 http://www.cs.swan.ac.uk/cie08/ Computability in Europe 2008: Logic and Theory of Algorithms University of Athens Athens, June 15-20 2008 PAPER SUBMISSION is now OPEN: http://www.cs.swan.ac.uk/cie08/submission.php Next message: [Nyaya] Forwarded announcement from Joe Halpern Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... More information about the Nyaya mailing list

20. Axiomatic Recursion Theory And The Continuous Functionals a higher type computation theory, and show that countable recursion over the this augmented set of schemes fails to generate countable recursion. http://projecteuclid.org/handle/euclid.jsl/1183741850

Log in RSS Title Author(s) Abstract Subject Keyword All Fields FullText more options Home Browse Search ... next Axiomatic Recursion Theory and the Continuous Functionals Simon Thompson Source: J. Symbolic Logic Volume 50, Issue 2 (1985), 442-450. Abstract We define, in the spirit of Fenstad [2], a higher type computation theory, and show that countable recursion over the continuous functionals forms such a theory. We also discuss Hyland's proposal from [4] for a scheme with which to supplement S1-S9, and show that this augmented set of schemes fails to generate countable recursion. We make another proposal to which the methods of this section do not apply. Full-text: Remote access If you are a member of the ASL, log in to Euclid for access. Full-text is available via JSTOR, for JSTOR subscribers. Go to this article in JSTOR. Links and Identifiers Permanent link to this document: http://projecteuclid.org/euclid.jsl/1183741850 JSTOR: links.jstor.org back to Table of Contents previous next Journal of Symbolic Logic Current Issue All Issues Search this Journal Editorial Board ... Log in RSS Cornell University Library

21. [ccl] CiE 2008 - 1st Call For Papers and extracting algorithms from proofs Higher type recursion theory and models * Effective descriptive set theory * Finite model theory * Formal http://www.mozart-oz.org/pipermail/ccl/2007-September/000230.html

[ccl] CiE 2008 - 1st Call for Papers Arnold Beckmann A.Beckmann at swansea.ac.uk Sat Sep 8 11:43:50 CEST 2007 Previous message: [ccl] M4M-5: Deadline Extension, 15th of September Next message: [ccl] ICALP 2008 - Second Call for Workshops Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] [Apologies for multiple copies] ****************************************************************** FIRST ANNOUNCEMENT AND CALL FOR PAPERS CiE 2008 http://www.cs.swan.ac.uk/cie08/ Previous message: [ccl] M4M-5: Deadline Extension, 15th of September Next message: [ccl] ICALP 2008 - Second Call for Workshops Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... More information about the ccl mailing list

22. Gmane -- Mail To News And Back Again Higher type recursion theory and applications Algorithmic game theory=20 models * Effective descriptive set theory * Finite model theory * Formal http://article.gmane.org/gmane.science.mathematics.prooftheory/466

Home Reading Searching Subscribe ... FAQ Sponsor A.Beckmann@... Subject: [PT] CiE 2008 - 1st Call for Papers Newsgroups: gmane.science.mathematics.prooftheory Date: 2007-09-08 09:43:50 GMT (15 weeks, 1 day, 21 hours and 43 minutes ago) [Apologies for multiple copies] * FIRST ANNOUNCEMENT AND CALL FOR PAPERS CiE 2008 http://www.cs.swan.ac.uk/cie08/ document.domain = 'gmane.org'; document.title = ' PT CiE 2008 1st Call for Papers';

23. Theories With Self-application And Computational Complexity Schwichtenberg, Higher type recursion, ramification and polynomial time, . Feferman, recursion theory and set theory a marriage of convenience, http://portal.acm.org/citation.cfm?id=942131.942136

24. The Journal Of Symbolic Logic, Volume 41 1824 BibTeX Julia F. Knight Omitting Types in set theory and Arithmetic. Equivalence of Some Definitions of recursion in a Higher Type Object. http://www.informatik.uni-trier.de/~ley/db/journals/jsyml/jsyml41.html

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

25. Logic And Language Links - Recursive Language higher type recursion theory recursion theory on ordinals Gloss Language (set of strings) for which the question of whether some string belongs to http://staff.science.uva.nl/~caterina/LoLaLi/Pages/135.html

Siblings tell me more... under formal language theory categorial grammar context free language Chomsky hierarchy phrase structure grammar ... feature constraint under recursion theory complexity of computation undecidability theory of numerations effectively presented structure ... TOP You have selected the concept recursive language Gloss: Language (set of strings) for which the question of whether some string belongs to the language is decidible. recursive language is a: subtopic of formal language theory subtopic of recursion theory recursive language has currently no subtopics. Long description: Not available yet. Search the hierarchy with v7 Caterina Caracciolo home page Home Search this site with Dowser Page generated on: 2004:9:7, 15:41 Information about LoLaLi.net Handbook Not available yet tell me more...

26. Set Theory Papers Of Andreas R. Blass We work in set theory without the axiom of choice, so infinite sums and products Needed Reals and recursion in Generic Reals (Ann. Pure Appl. Logic 109 http://www.math.lsa.umich.edu/~ablass/set.html

Set Theory Papers Andreas Blass The papers are listed in reverse chronological order, except that I put two surveys at the beginning to make them easier to find. Nearly Countable Cardinals PostScript or PDF An expository talk, for a general mathematical audience, about cardinal characteristics of the continuum. Combinatorial Cardinal Characteristics of the Continuum (to appear as a chapter in the Handbook of Set Theory (ed. M. Foreman, M. Magidor, and A. Kanamori)) PostScript or PDF This survey of the theory of cardinal characteristics of the continuum is to appear as a chapter in the "Handbook of Set Theory." As the title indicates, I concentrate on the combinatorial characteristics; Tomek Bartoszynski has written a chapter on the category and measure characteristics. Voting Rules for Infinite Sets and Boolean Algebras PDF A voting rule in a Boolean algebra B is an upward closed subset that contains, for each element x in B, exactly one of x and -x. We study several aspects of voting rules, with special attention to their relationship with ultrafilters. In particular, we study the set-theoretic hypothesis that all voting rules in the Boolean algebra of subsets of the natural numbers modulo finite sets are nearly ultrafilters. We define the notion of support of a voting rule and use it to describe voting rules that are, in a sense, as different as possible from ultrafilters. Finally, we consider how much of the axiom of choice is needed to guarantee the existence of voting rules.

27. Foundations Of Mathematics A History of set theory from School of Mathematical and Computational Sciences, .. Introduction to Logic and recursion theory - by Edward Boyden, http://sakharov.net/foundation_rt.html

Home Alexander Sakharov Irina Tim Projects Resources Sport Photos Median Logic Math Foundations Badminton Clubs Trip Photos ... Downloads Foundations of Mathematics - Textbook / Reference - with contributions by Bhupinder Anand Harvey Friedman Haim Gaifman Vladik Kreinovich ... Stephen Simpson featured in the Computers/Mathematics section of Science Magazine NetWatch This is an online resource center for materials that relate to foundations of mathematics (FOM). It is intended to be a textbook for studying the subject and a comprehensive reference. As a result of this encyclopedic focus, materials devoted to advanced research topics are not included. The author has made his best effort to select quality materials on www. This reference center is organized as a book as opposed to an encyclopedia dictionary directory , or link collection . This page represents book's contents page. One can use this page to study the foundations of mathematics by reading topics following the links in their order or jumping over certain chapters. Where appropriate, topics covered in the referred web resource are listed under the link. In particular, it is done if the resource covers more than the respective section heading and title suggest. Presumably, this is the only anchor page one needs to navigate all math foundations topics. I believe you can even save some $$ because the materials listed here should be sufficient, and you do not have to buy a book or two. The links below are marked in order to indicate the type of material:

28. RISC : Detail D'une Nouvelle De La Liste Echos theory, Higher Type recursion theory, Domain theory and Category recursively measurable set of the real line with respect to the Lebesgue measure. http://www.risc.cnrs.fr/detail_lesechos.php?ID=6662

29. Abstract Stone Duality Hence classical recursion theory, which was formulated in a very and it takes a hundred or so pages of a textbook such as 26to set out the details of http://www.monad.me.uk/ASD/manifesto.php

Abstract Stone Duality Paul Taylor Summary Computer science has enjoyed topological interpretations for thirty years, but arbitrary infinite joins have precluded the converse, a computational interpretation of general topology. Abstract Stone Duality (ASD) is a type theory in which the topology on a space is an exponential with a lambda-calculus, not an infinitary lattice. But instead of rewriting old proofs in a pre-conceived logic, it exploits a deep mathematical theme, Stone duality, reconciling conceptual and computational traditions in mathematics. ASD gives a computational interpretation to continuous functions, not only for domains but between all locally compact spaces, including those from geometry. Published work develops the necessary infrastructure, defining notions such as compact Hausdorff spaces very naturally, with lattice duality between open and closed phenomena. Recent work generalises interval analysis from R to other spaces, but the intervals themselves are only mentioned during compilation. The categorical structure allows a conceptual development, whilst the lambda-calculus handles higher types. This will be used to investigate differential and integral calculus.

30. [PVS] CiE 2008 - 1st Call For Papers Higher type recursion theory and applications Algorithmic game theory models * Effective descriptive set theory * Finite model theory * Formal http://pvs.csl.sri.com/mail-archive/pvs/msg03666.html

Date Prev Date Next Thread Prev Thread Next ... Thread Index [PVS] CiE 2008 - 1st Call for Papers To : undisclosed-recipients: ; Subject : [PVS] CiE 2008 - 1st Call for Papers From Date : Sat, 8 Sep 2007 10:43:50 +0100 (BST) 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 Organization : Swansea University (http://www.swansea.ac.uk/) Sender [Apologies for multiple copies] ****************************************************************** FIRST ANNOUNCEMENT AND CALL FOR PAPERS CiE 2008 http://www.cs.swan.ac.uk/cie08/ Prev by Date: [PVS] Associate Professor Position in Formal Methods at theUniversity of Oslo, Norway Next by Date: [PVS] CAV 2008: Call for Workshops Prev by thread: [PVS] Associate Professor Position in Formal Methods at theUniversity of Oslo, Norway

31. [Coq-Club] CiE08 - 2nd Call For Papers Nijmegen, and M. Seisenberger, Swansea) Higher type recursion theory and models * Effective descriptive set theory * Finite model theory * Formal http://pauillac.inria.fr/pipermail/coq-club/2007/003216.html

[Coq-Club] CiE08 - 2nd Call for Papers Arnold Beckmann A.Beckmann at !NS! swansea.ac.uk Mon, 19 Nov 2007 08:04:54 +0000 Previous message: [Coq-Club] SSReflect not cooperating Next message: [Coq-Club] Calculemus 2008: First Call for Papers Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] [Apologies for multiple copies] ****************************************************************** SECOND CALL FOR PAPERS CiE 2008 http://www.cs.swan.ac.uk/cie08/ Computability in Europe 2008: Logic and Theory of Algorithms University of Athens Athens, June 15-20 2008 PAPER SUBMISSION is now OPEN: http://www.cs.swan.ac.uk/cie08/submission.php Previous message: [Coq-Club] SSReflect not cooperating Next message: [Coq-Club] Calculemus 2008: First Call for Papers Messages sorted by: [ date ] [ thread ] [ subject ] [ author ]

32. List Of Invited Speakers A.1 Mathematical logic (proof theory, recursion theory, model theory, set theory). J. Bagaria (U. Barcelona and ICREA, Spain), Natural Axioms for set http://www.uniovi.es/Congresos/2003/DLMPS/Structure/Speakers.htm

Invited Speakers :: state August 4 (more to be added shortly as acceptations arrive ) Plenary Lectures 2. Invited Speakers by Section A. Logic B. General Philosophy of Science C. Philosophical Issues of Particular Sciences D. Ethical, Social, and Historical Perspectives on Philosophy of Science Special Symposia Affiliated Symposia ... PLENARY LECTURES M. Garrido-Giménez (Spain), "The New Scientific Image of Man and Philosophy". M. O. Rabin (Harvard U., USA), "Proofs and Persuasions from Computer Science". E. Sober (U. Wisconsin, USA), "Intelligent Design is Unestable. What about Natural Selection?" W. H. Woodin (U. California at Berkeley, USA), "The Axioms for Set Theory: Then and Now" INVITED SPEAKERS BY SECTION The Congress is divided into several sections which represent different areas of logic, methodology and philosophy of science. The 12th Congress (2003) will comprise the following sections: A LOGIC A.1 Mathematical logic (proof theory, recursion theory, model theory, set theory)

33. Conference On Logic, Computability And Randomness The Medvedev lattice is a structure from computability theory with ties to with nrandomness in the both recursion theory and set theory aspects. http://www.dc.uba.ar/people/logic2007/

Conference on Logic, Computability and Randomness January 10-13, 2007 Buenos Aires, Argentina program committee submission local organizers plenary speakers ... conference address The theme of the conference will be algorithmic randomness and related topics in logic, computability and complexity. The program will consist of invited talks contributed talks 3 introductory courses. NEW! Check here The booklet with the abstracts of invited and contributed talks is available here See the poster of the conference in jpg or ... YPF Foundation , located in the biggest park in Buenos Aires "los bosques de Palermo" (very near the University campus, Facultad de Ciencias Exactas y Naturales Universidad de Buenos Aires The meeting is sponsored by the Association for Symbolic Logic There is no registration fee. Student members of the ASL can apply for travel grants (the approval process takes a few weeks). The spirit of the Conference will be the same as earlier meeting in Córdoba, 2004. The booklet with the abstracts of invited and contributed talks of the earlier meeting is available here If you wish to attend to the conference (and you are not giving a talk) please let us know in advance.

34. Lars Birkedal / Realizability Bibliography Church s thesis, continuity and set theory. Journal of Symbolic Logic In J.N. Crossley, editor, sets, Models, and recursion theory , pages 309331. http://www.itu.dk/people/birkedal/realizability/index.html

Realizability Bibliography This bibliography on realizability has been established in connection with the Workshop on Realizability Semantics and Applications 1999 in Trento, Italy. Additions and corrections are very welcome. Please email them to Lars Birkedal ( birkedal@itu.dk BibTeX database: realizability.bib Search the Bibliography Keywords: Authors: 345 references, last updated Tue Jun 13 8:59:00 2000 M . Abadi and G.D. Plotkin. A per model of polymorphism and recursive types . In J. Mitchell, editor, 5th Annual IEEE Symposium on Logic in Computer Science , pages 355-365, Philadelphia, 1990. IEEE Computer Society Press. M . Abadi and L. Cardelli. A Theory of Objects . Springer Verlag, 1996. S . Abramsky. Typed realizability . Talk at the workshop on Category Theory and Computer Science in Cambridge, England, August 1995. P .H.G. Aczel. A note on interpreting intuitionistic higher-order logic , 1980. Handwritten note. T . Altenkirch. Constructions, Inductive Types and Strong Normalization . PhD thesis, University of Edinburgh, 1993. Available as report ECS-LFCS-93-279.

35. One Hundred Years Of Russell's Paradox - Abstracts This distinction is analogous to the arithmetic and analytic hierarchies familiar in recursion theory and descriptive set theory. http://www.lrz-muenchen.de/~russell01/papers.html

Abstracts The following papers have so far been announced: We present an approximation space (U,R) which is an infinite (hypercontinuum) solution to the domain equation U isomorphic to C(R), (U, c: U-> U, i: U-> U), where c(u) = Union [u]_R and i(u)= Intersection [u]_R. John Bell Russell's Paradox and Diagonalization in a Constructive Context One of the most familiar uses of the Russell paradox, or, at least, of the idea underlying it, is in proving Cantor's theorem that the cardinality of any set is strictly less than that of its power set. The other method of proving Cantor's theorem-employed by Cantor himself in showing that the set of real numbers is uncountable-is that of diagonalization. Typically, diagonalization arguments are used to show that function spaces are "large" in a suitable sense. Classically, these two methods are equivalent. But constructively they are not: while the argument for Russell's paradox is perfectly constructive, (i.e. employs on intuitionistically acceptable principles of logic) the method of diagonalization fails to be so. In my paper I shall describe the ways in which these two methods diverge in a constructive setting. Ulrich Blau The Significance of the Largest and Smallest Numbers for the Oldest Paradoxes Wilfried Buchholz On Gentzen's consistency proofs for arithmetic Gentzen has given three consistency proofs for arithmetic: "Der erste Widerspruchsfreiheitsbeweis fuer die klassische Zahlentheorie", Galley proof of sections IV and V of Gentzen 1936, Archiv Math.Logik 16(1974)

36. Downloadable Publications Constructive natural deduction and its omegaset interpretation. The Lambda-Calculus connections to higher type recursion theory, Proof-theory, http://www.di.ens.fr/users/longo/download.html

Selected publications by Giuseppe Longo available as .dvi, .ps (some gzipped) or .pdf files by ftp 1 - Mathematical Logic and Computer Science; 2 - Cognition and Foundations of Mathematical Knowledge; 3 - Morphological Information and Complexity; 4 - Minima philosophica. 1 - Mathematical Logic and Computer Science (for about 70 more papers see publicationsNov06.pdf Title Download in dvi gz or pdf format Download in ps or ps gz format Book: Andrea Asperti and Giuseppe Longo. Categories, Types and Structures . Category Theory for the working computer scientist. M.I.T. Press, 1991 (pp. 1 - 300) (currently out of print and downloadable upon kind permission of the M.I.T. Press The entire book (.pdf) The entire book (.ps-tar) Chapter-by-chapter: Ch.1 Ch.2 Ch.3 Ch.4 ... Ch.12 Giuseppe Longo and Eugenio Moggi A Category-theoretic characterization of functional completeness. . Theoretical Computer Science , 70 (2), 1990, pp.193-211. funct-compl.ps.gz Luca Cardelli and Giuseppe Longo A semantic basis for Quest.

37. The Extent Of Constructive Game Labellings Löwe And Semmes We just assume naïve set theory and provide all necessary definitions and 1982Summer Institute on recursion theory, Held at Cornell University, http://logcom.oxfordjournals.org/cgi/content/full/exl039v1?ck=nck

38. JSTOR $\beta$-Recursion Theory. These considerations have led to further progress in other areas of generalized recursion theory, arecursion theory and recursion in higher type objects. http://links.jstor.org/sici?sici=0022-4812(198109)46:3<664:T>2.0.CO;2-4

39. Type Theory - Wikipedia, The Free Encyclopedia set theories whose point of departure is type theory, but whose axioms, ontology, respectively, and defines the set of types recursively as follows http://en.wikipedia.org/wiki/Type_theory

var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia"; Type theory From Wikipedia, the free encyclopedia Jump to: navigation search In mathematics logic and computer science type theory is any of several formal systems that can serve as alternatives to naive set theory , or the study of such formalisms in general. In programming language theory , a branch of computer science type theory can refer to the design, analysis and study of type systems , although some computer scientists limit the term's meaning to the study of abstract formalisms such as typed λ-calculi Bertrand Russell invented the first type theory in response to his discovery that Gottlob Frege 's version of naive set theory was afflicted with Russell's paradox . This type theory features prominently in Whitehead and Russell 's Principia Mathematica . It avoids Russell's paradox by first creating a hierarchy of types, then assigning each mathematical (and possibly other) entity to a type. Objects of a given type are built exclusively from objects of preceding types (those lower in the hierarchy), thus preventing loops. Alonzo Church , inventor of the lambda calculus , developed a higher-order logic commonly called Church's Theory of Types , in order to avoid the Kleene-Rosser paradox afflicting the original pure lambda calculus. Church's type theory is a variant of the lambda calculus in which expressions (also called formulas or λ-terms) are classified into types, and the types of expressions restrict the ways in which they can be combined. In other words, it is a

40. Longo Symposium In this perspective, Longo worked at some aspects of recursion theory, Higher Type recursion theory, Domain theory and Category theory as part of a unified http://www.pps.jussieu.fr/~gc/other/rdp/talks.html

28-29 June 2007 From Type Theory to Morphologic Complexity: A Colloquium in Honor of Giuseppe Longo In conjunction with RDP 2007 Paris, Conservatoire National des Arts et M©tiers , Amphitheaters 3 and A. This colloquium was organised to celebrate the 60th birthday of Giuseppe Longo . Some photos of the meeting can be found here The main research area Giuseppe Longo has been interested in concerns syntactic and semantic properties of the "logical base" of functional languages: Combinatory Logic, Lambda-calculus and their extensions. However, he always investigated these topics in its broadest setting which relates them to Recursion Theory, Proof Theory and Category Theory. In this perspective, Longo worked at some aspects of Recursion Theory, Higher Type Recursion Theory, Domain Theory and Category Theory as part of a unified mathematical framework for the theory and the design of functional languages. In a sense, Longo has always been mostly interested in the "interconnecting results" or "bridges" and applications among different areas and to language design. He also worked at the applications of functional approaches to Object-Oriented programming. He is currently extending his interdisciplinary interests to Philosophy of Mathematics and Cognitive Sciences. A recent interdisciplinary project on Geometry and Cognition (started with the corresponding grant: "G©om©trie et Cognition", 1999 - 2002 with J. Petitot et B. Teissier), focused on the geometry of physical and biological spaces. The developements of this project lead to a new initiative at DI-ENS, in 2002, the setting up of the research team "Complexit© et information morphologiques" (CIM), centered on foundational problems in the interface between Mathematics, Physics and Biology.

41. A List Of Papers On Complexity At Higher Types This is one of the earliest uses of subrecursive Highertype recursion. . A. Seth, Complexity theory of Higher Type Functionals, Ph.D. Thesis, http://www.cis.syr.edu/~royer/bib2.html

A List of Papers on Computational Complexity at Higher Types and Related Topics with sporadic updates since then (Version 3 will be out one of these days.) The following was originally built from the list of papers for my Spring 97 course Computation and Complexity at Higher Types. Papers Surveys Papers before 1989 Studies of the BFFs and related classes Characterizing complexity classes via categorical constructs, lambda-calculi, logics, and types ... Illustrations by Gustave Dore (Since this is the web, of course there must be pictures.) Surveys R. Gandy and J. Hyland, Computable and recursively countable functions of higher type, in Logic Colloquium 76, North-Holland (1977) 407-438. This covers higher-type computability. S. Cook, Computability and complexity of higher type functions, in Logic from Computer Science (Y.N. Moschovakis, ed.), Springer-Verlag (1991) 51-72. This covers higher-type computing and complexity and contains some interesting original results, e.g., the quasi-linear ordering functional. A reasonable starting point for learning about higher types and complexity.

42. Wikiseek - Ultra Effective descriptive set theory recursion theory Hierarchy Mathematical logic set theory, the analytical hierarchy is a higher type analogue of the http://www.wikiseek.com/results.php?q=Type hierarchies, logic

43. Feferman: Recursion In Total Functionals Of Finite Type Rather one wants to allow the set of terms to increase as the stock of .. Thus a recursion theory based on IVI should also have good properties. http://www.numdam.org/numdam-bin/fitem?id=CM_1977__35_1_3_0

44. Type Theory ST reveals how type theory can be made very similar to axiomatic set theory. . system · set theory · Proof theory · Model theory · recursion theory http://wapedia.mobi/en/Type_Theory

Wiki: Type theory Control your debt - click to call (Ad) Contents: 1. Simple theory of types 2. History of type theory 3. Practical impact of type theory 3. 1. Computing ... Wapedia: For Wikipedia on mobile phones

45. Gmane.science.mathematics.prooftheory This is a mailing list devoted to proof theory. headers algorithms from proofs Higher type recursion theory and applications Algorithmic game theory=20 http://permalink.gmane.org/gmane.science.mathematics.prooftheory/466

This is a mailing list devoted to proof theory. headers Arnold Beckmann 8 Sep 11:40 [PT] CiE 2008 - 1st Call for Papers A.Beckmann@... Subject: [PT] CiE 2008 - 1st Call for Papers Newsgroups: gmane.science.mathematics.prooftheory Date: 2007-09-08 09:43:50 GMT [Apologies for multiple copies] * FIRST ANNOUNCEMENT AND CALL FOR PAPERS CiE 2008 http://www.cs.swan.ac.uk/cie08/ Permalink Reply Navigate Go to gmane. science. mathematics. prooftheory Topic Go to the topic Project Web Page This is a mailing list devoted to proof theory. Search Archive Advertisement Language Change language Options Current view: Threads only / Showing whole messages / Not hiding cited text. Change to All messages, shortened messages , or hide cited text Post a message NNTP Newsgroup Classic Gmane web interface RSS Feed List Information About Gmane Gmane

46. Cornell Math - Fall 2002 Course Descriptions Also considers Polya theory action of a group on a set, Burnside lemma, DeBruijn s method, . MATH 784 recursion theory. Richard A. Shore. 4 credits. http://www.math.cornell.edu/Courses/Fall/FA02descr.html

Fall 2002 Course Descriptions MATH 103: Mathematical Explorations Homer White, Beverly West. 3 credits. This course is for students who wish to experience how mathematical ideas naturally evolve. The homework consists of the students actively investigating mathematical ideas. The course emphasizes ideas and imagination as opposed to techniques and calculations. Topics vary depending on the instructor and are announced (www.math.cornell.edu) several weeks before the semester begins. Some assessment is done through writing assignments. More info to come. Lecture 03: Iterations and Patterns, Beverly West Required text: ONE of the following (parallel assignments will be given) Peak and Frame, W. H. Freeman, 1994 (ISBN: 0-7167-2429-4). OR Stewart, Ian, Does God Play Dice? (Edition 2) Blackwell, 2002 The syllabus for Lecture 3 spends roughly 4 weeks each on * iterating real-valued functions; * geometric iteration;

47. Tulane Math Colloquium: Fall 2005 Does geometry need a full set theory, therefore? In giving a negative answer, we shall consider Highertype sets introduced by parametric definitions with http://www.math.tulane.edu/activities/colloquium/Spring_2006.html

Home Office hours Weekly activities Find people ... Summer research Lectures... Colloquium: Spring 2006 Go to... Lectures... Colloquium index Vigre seminars Undergrad seminar ... Clifford lectures All talks are in Gibson 414 at 3:30 P.M. unless otherwise noted. Refreshments in Gibson 426 after the talk. Spring 2006 C omments indicating vacations, special lectures, or change in location or time are made in red January 19 Speaker, Institution "Title" Abstract: January 26 Thomas A. Garrity, Willians University "On Writing Numbers: Multidimensional Continued Fractions and the Hermite Problem" Abstract: February 2 Dana S. Scott, Carnegie Mellon University "Parametric sets and virtual classes" Abstract: In an axiomatic development of geometry, there is much convenience to be found in treating various loci as sets. Thus, a line corresponds to the set of all points lying on the line; a circle, to the set of all points on the circumference. Moreover, sets of sets are natural, say in considering pencils of lines or circles or conics. And families of pencils are used as well. Does geometry need a full set theory, therefore? In giving a negative answer, we shall consider higher-type sets introduced by parametric definitions with just finite lists of points as parameters. We will show how to formulate a simple axiomatization for such sets together with a notation for virtual classes. The objective is to have the USE of set-theoretical notations without the ONTOLOGY of higher-type logic or Zermelo- Fraenkel set theory.

48. CiE 2007 - Conference Description set theory; Finite model theory; Formal aspects of program analysis; Formal methods; Foundations of computer science; Games; Generalized recursion http://www.amsta.leeds.ac.uk/~pmt6sbc/cie07.descr.html

CiE 2007 General Information Participation Scientific Programme ... CCA 2007 Conference Description Conference themes: Computability has played a crucial role in mathematics and computer science, leading to the discovery, understanding and classification of decidable/undecidable problems, paving the way to the modern computer era, and affecting deeply our view of the world. Recent new paradigms of computation, based on biological and physical models, address in a radically new way questions of efficiency and challenge assumptions about the so-called Turing barrier. CiE 2007 will address various aspects of the ways computability and theoretical computer science enable scientists and philosophers to deal with mathematical and real world issues, ranging through problems related to logic, mathematics, physical processes, real computation and learning theory. At the same time it will focus on different ways in which computability emerges from the real world, and how this affects our way of thinking about everyday computational issues. Conference Topics: These include, but not exclusively -

49. Alternative Axiomatic Set Theories (Stanford Encyclopedia Of Philosophy) By alternative set theories we mean systems of set theory differing significantly for the development of an extension of recursion theory to sets. http://plato.stanford.edu/entries/settheory-alternative/

Cite this entry Search the SEP Advanced Search Tools ... Please Read How You Can Help Keep the Encyclopedia Free Alternative Axiomatic Set Theories First published Tue 30 May, 2006 By "alternative set theories" we mean systems of set theory differing significantly from the dominant ZF (Zermelo-Frankel set theory) and its close relatives (though we will review these systems in the article). Among the systems we will review are typed theories of sets, Zermelo set theory and its variations, New Foundations and related systems, positive set theories, and constructive set theories. An interest in the range of alternative set theories does not presuppose an interest in replacing the dominant set theory with one of the alternatives; acquainting ourselves with foundations of mathematics formulated in terms of an alternative system can be instructive as showing us what any set theory (including the usual one) is supposed to do for us. The study of alternative set theories can dispel a facile identification of "set theory" with "Zermelo-Fraenkel set theory"; they are not the same thing. 1. Why set theory?

50. FOM: Concepts Of Recursion Theory The full importance of recursions in recursion theory only became apparent with the introduction by Kleene of recursive function of higher type objects. http://cs.nyu.edu/pipermail/fom/1998-August/002024.html

FOM: Concepts of Recursion Theory Joseph Shoenfield jrs at math.duke.edu Sat Aug 29 15:21:36 EDT 1998 Previous message: FOM: On "grasping" Con(ZFC) Next message: FOM: Concepts of Recursion Theory (reply to Shoenfield) Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Previous message: FOM: On "grasping" Con(ZFC) Next message: FOM: Concepts of Recursion Theory (reply to Shoenfield) Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... More information about the FOM mailing list

51. Peter Clote's Publications Applications of the low basis theorem in arithmetic , Springer Lecture Notes in Mathematics 1141,recursion theory Week, Proceedings Oberwolfach 1984, ed. http://clavius.bc.edu/~clote/publications.html

Publications Table of Contents Books Journal Articles Refereed Articles in Books Refereed Articles in Proceedings Books Boolean Functions and Models of Computation , by P. Clote and E. Kranakis, 615 pages, Springer-Verlag, 2003, ISBN: 3-540-59436-1 (hardcover). Computational Molecular Biology: An Introduction Japanese translation of Computational Molecular Biology: An Introduction , P. Clote and R. Backofen (2005). Computer Science Logic , by P. Clote and H. Schwichtenberg (Eds.), 14th International Workshop, CSL 2000, Springer Lecture Notes in Computer Science , ISBN 3-540-67895-6, August 2000. Arithmetic, Proof Theory and Computational Complexity , Oxford University Press, eds. P. Clote and J. Krajicek (1993). Feasible Mathematics II Research monograph translation, Theory of Relations Back to Table of Contents Journal Articles Proteins: Structure, Function and Bioinformatics , to appear. Nucleic Acids Res. , Web Server Issue (2006), in press. DiANNA 1.1: An extension of the DiANNA web server for ternary cysteine classification, F. Ferre, P. Clote, Nucleic Acids Res.

52. All For You All For Me - ‹³‰È‘ Translate this page , , , 1989 , recursion theory degree 2003, Association for symbolic logic, higher type computability http://homepage1.nifty.com/miya-miya/cs/index.html

“Ç‚ñ‚¾ŒvŽZ‹@‰ÈŠw‚Ì‹³‰È‘‚ð‹L˜^‚µ‚Ä‚¢‚«‚Ü‚· Title Author Publisher Date Comments Mathematical Logic Joseph R. Shoenfield Addison Wesley Longman ”—˜_—Šw‚Ì“ü–发 The Formal Semantics of Programming Languages Glynn Winskel MIT Press Symbolic Logic and Mechanical Theorem Proving Chin-Liang Chang Richard Char-Tung Lee Academic Pr First Order Logic‚̉ðà‘ Modern Compiler Implementation in ML Andrew W. Appel Cambridge University Press ML‚à ‚ÌƒRƒ“ƒpƒCƒ‰[‚ÌŽd‘g‚Ý communicating and mobile systems:the pi-calculus Robin Milner Cambridge Univ Pr pi-calculus‚̉ðà‘ ‚‹´³Žq ‹ß‘ã‰ÈŠwŽÐ Œ^‚È‚µƒÉŒvŽZ‚Ì“ü–发 Types and Programming Languages Benjamine C. Pierce MIT Press Œ^•t‚«ƒÉŒvŽZ‚Ì“ü–发 Logic and Structure D. van Dalen Springer-Verlag ˆêŠKqŒê˜_—‚̏ؖ¾˜_Aƒ‚ƒfƒ‹‚Ì—˜_‚Ì“ü–发B Proofs and Types J.-Y. Girard, Y. Lafont and P. Taylor Cambridge University Press Ø–¾˜_AŒ^—˜_‚Æ‚»‚̈Ӗ¡˜_ Recursion Theory Joseph R. Shoenfield A K Peters Ltd Recursion Theory —l‘Š˜_—“ü–å G.E.ƒqƒ [ƒY M.J.ƒNƒŒƒXƒEƒFƒ‹ P¯ŽÐŒú¶‘Št —l‘Š˜_—Šw‚Ì“ü–发 Handbook of proof theory Buss North-Holland Ø–¾˜_ARealizability Categories for Types Roy L. Crole