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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

 3. MathNet-Mathematical Subject Classification 03D60, recursion theory on ordinals, admissible sets, etc. 03D65, Highertype and set recursion theory. 03D70, Inductive definabilityhttp://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
##### 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
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 2000http://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
##### 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 theoryhttp://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
##### 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/

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 andhttp://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 ZMATHhttp://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 theoryhttp://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 andhttp://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
##### CiE08 - 2nd Call for Papers
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##### 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 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 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
• Home Browse Search ... next
##### Axiomatic Recursion Theory and the Continuous Functionals
Simon Thompson Source: J. Symbolic Logic Volume 50, Issue 2 (1985), 442-450.
##### Journal of Symbolic Logic

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 [Apologies for multiple copies] ****************************************************************** FIRST ANNOUNCEMENT AND CALL FOR PAPERS CiE 2008 http://www.cs.swan.ac.uk/cie08/ 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
##### Volume 41, Number 1, March 1976

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 under recursion theory 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
##### 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
##### - 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
##### 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
##### [PVS] CiE 2008 - 1st Call for Papers
[Apologies for multiple copies] ****************************************************************** FIRST ANNOUNCEMENT AND CALL FOR PAPERS CiE 2008 http://www.cs.swan.ac.uk/cie08/

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 [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

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-GimÃ©nez (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 CÃ³rdoba, 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)
Constructive natural deduction and its omegaset interpretation. The Lambda-Calculus connections to higher type recursion theory, Proof-theory,
##### 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
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 LÃ¶we And Semmes We just assume naÃ¯ve 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
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 ÃÂ»-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 ÃÂ»-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 MÂ©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: "GÂ©omÂ©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 "ComplexitÂ© 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
##### 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.

 42. Wikiseek - Ultra Effective descriptive set theory recursion theory Hierarchy Mathematical logic set theory, the analytical hierarchy is a higher type analogue of thehttp://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 Â· set theory Â· Proof theory Â· Model theory Â· 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
This is a mailing list devoted to proof theory. headers Arnold Beckmann 8 Sep 11:40
##### [PT] CiE 2008 - 1st Call for Papers
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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
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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
##### 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 ...
##### 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.

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

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
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