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1. 03E: Set Theory Fuzzy set theory replaces the twovalued set-membership function with a real-valued Nonclassical and second-order set theories; 03E72 Fuzzy set theory http://www.math.niu.edu/~rusin/known-math/index/03EXX.html

Search Subject Index MathMap Tour ... Help! ABOUT: Introduction History Related areas Subfields POINTERS: Texts Software Web links Selected topics here 03E: Set theory Introduction Naive set theory considers elementary properties of the union and intersection operators Venn diagrams, the DeMorgan laws, elementary counting techniques such as the inclusion-exclusion principle, partially ordered sets, and so on. This is perhaps as much of set theory as the typical mathematician uses. Indeed, one may "construct" the natural numbers, real numbers, and so on in this framework. However, situations such as Russell's paradox show that some care must be taken to define what, precisely, is a set. However, results in mathematical logic imply it is impossible to determine whether or not these axioms are consistent using only proofs expressed in this language. Assuming they are indeed consistent, there are also statements whose truth or falsity cannot be determined from them. These statements (or their negations!) can be taken as axioms for set theory as well. For example, Cohen's technique of forcing showed that the Axiom of Choice is independent of the other axioms of ZF. (That axiom states that for every collection of nonempty sets, there is a set containing one element from each set in the collection.) This axiom is equivalent to a number of other statements (e.g. Zorn's Lemma) whose assumption allows the proof of surprising even paradoxical results such as the Banach-Tarski sphere decomposition. Thus, some authors are careful to distinguish results which depend on this or other non-ZF axioms; most assume it (that is, they work in ZFC Set Theory).

2. 03Exx 03E30 Axiomatics of classical set theory and its fragments 03E70 Nonclassical and secondorder set theories; 03E72 Fuzzy set theory http://www.ams.org/msc/03Exx.html

Home MathSciNet Journals Books ... Contact Us 201 Charles Street Providence, RI 02904 USA Phone: 401-455-4000 or 800-321-4AMS Or email us at ams@ams.org Open Positions Prev: Set theory 03E02 Partition relations 03E04 Ordered sets and their cofinalities; pcf theory 03E05 Other combinatorial set theory 03E10 Ordinal and cardinal numbers 03E15 Descriptive set theory [See also 03E17 Cardinal characteristics of the continuum 03E20 Other classical set theory (including functions, relations, and set algebra) 03E25 Axiom of choice and related propositions 03E30 Axiomatics of classical set theory and its fragments 03E35 Consistency and independence results 03E40 Other aspects of forcing and Boolean-valued models 03E45 Inner models, including constructibility, ordinal definability, and core models 03E47 Other notions of set-theoretic definability 03E50 Continuum hypothesis and Martin's axiom 03E55 Large cardinals 03E60 Determinacy principles 03E65 Other hypotheses and axioms 03E70 Nonclassical and second-order set theories 03E72 Fuzzy set theory 03E75 Applications of set theory 03E99 None of the above, but in this section

3. Mhb03.htm 03E70, Nonclassical and secondorder set theories. 03E72, Fuzzy set theory. 03E75, Applications of set theory. 03E99, None of the above, but in this section 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.)

4. HeiDOK 03E70 Nonclassical and secondorder set theories ( 0 Dok. ) 03E72 Fuzzy set theory ( 0 Dok. ) 03E75 Applications of set theory ( 0 Dok. http://archiv.ub.uni-heidelberg.de/volltextserver/msc_ebene3.php?zahl=03E&anzahl

5. 03Exx Ordinal and cardinal numbers 03E15 Descriptive set theory See also 28A05, 03E70 Nonclassical and secondorder set theories 03E72 Fuzzy set theory http://www.emis.de/MSC2000/03Exx.html

Set theory 03E02 Partition relations 03E04 Ordered sets and their cofinalities; pcf theory 03E05 Other combinatorial set theory 03E10 Ordinal and cardinal numbers 03E15 Descriptive set theory [See also ] 03E17 Cardinal characteristics of the continuum 03E20 Other classical set theory (including functions, relations, and set algebra) 03E25 Axiom of choice and related propositions 03E30 Axiomatics of classical set theory and its fragments 03E35 Consistency and independence results 03E40 Other aspects of forcing and Boolean-valued models 03E45 Inner models, including constructibility, ordinal definability, and core models 03E47 Other notions of set-theoretic definability 03E50 Continuum hypothesis and Martin's axiom 03E55 Large cardinals 03E60 Determinacy principles 03E65 Other hypotheses and axioms 03E70 Nonclassical and second-order set theories 03E72 Fuzzy set theory 03E75 Applications of set theory 03E99 None of the above, but in this section Version of December 15, 1998

6. 03Exx 03E65, Other hypotheses and axioms. 03E70, Nonclassical and secondorder set theories. 03E72, Fuzzy set theory. 03E75, Applications of set theory http://www.impan.gov.pl/MSC2000/03Exx.html

Set theory Partition relations Ordered sets and their cofinalities; pcf theory Other combinatorial set theory Ordinal and cardinal numbers Descriptive set theory [See also Cardinal characteristics of the continuum Other classical set theory (including functions, relations, and set algebra) Axiom of choice and related propositions Axiomatics of classical set theory and its fragments Consistency and independence results Other aspects of forcing and Boolean-valued models Inner models, including constructibility, ordinal definability, and core models Other notions of set-theoretic definability Continuum hypothesis and Martin's axiom Large cardinals Determinacy principles Other hypotheses and axioms Nonclassical and second-order set theories Fuzzy set theory Applications of set theory None of the above, but in this section

7. List KWIC DDC22 510 And MSC+ZDM E-N Lexical Connection set theories Nonclassical and secondorder 03E70 set theory 511.322 set theory 03Exx set theory applications of 03E75 set theory descriptive 03E15 http://www.math.unipd.it/~biblio/kwic/msc-cdd/dml2_11_51.htm

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, power series. convergence, summability (infinite products, integrals) # sequences and series, series of functions # power series, singular integrals # conjugate functions, conjugate series, summability # sequences, 40-XX series, transformations, transforms, operational calculus, etc. # analytical theory: series. convergence, summability (infinite products, integrals) # sequences and series, power series; Weil representation # theta Serre spectral sequences service # queues and sesquilinear, multilinear) # forms (blilinear, set (change of topology, comparison of topologies, lattices of topologies) # several topologies on one set algebra set algebra) # other classical set theory (including functions, relations, and set contractions, etc.) # nonexpansive mappings, and their generalizations (ultimately compact mappings, measures of noncompactness and condensing mappings, $A$-proper mappings, $K$-

8. Sachgebiete Der AMS-Klassifikation: 00-09 03C52 Properties of classes of models 03C55 settheoretic model theory 03C57 hypotheses and axioms 03E70 Nonclassical and second-order set theories 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

9. DC MetaData For: Towards Quantum Mathematics Part II: Manifold Notions MSC 03E70 Nonclassical and secondorder set theories 18D05 Double categories, $2$-categories, bicategories, hypercategories 18G50 Nonabelian homological http://www.esi.ac.at/Preprint-shadows/esi556.html

Karl-Georg Schlesinger Towards Quantum Mathematics Part II: Manifold Notions Preprint series: ESI preprints MSC 03E70 Nonclassical and second-order set theories 18D05 Double categories, $2$-categories, bicategories, hypercategories 18G50 Nonabelian homological algebra 81P10 Logical foundations of quantum mechanics 83C27 Lattice gravity, Regge calculus and other discrete methods PACS: 02.10.Cz,02.10.Ws,03.65.Ca,04.60.Nc Abstract Here we use the language of quantum set theory, developed in Part I of this work, to explore quantized (i.e. categorified) manifold notions. We first deal with the differentiable structure in the sense of an infinitesimal patching of tangent spaces and arrive at the (finite-dimensional) representations of (higher) groupoids this way. The relation to TQFT and to prev ious work of the author on a quantization of the category of topological spaces and continuous injections is pointed out. In a second approach, we deal with the topological level, first discretized by a triangulation and then in an easy to grasp continuous analog of this. Here, we are lead to

10. PlanetMath: Neutrosophic Set The notion of neutrosophic set was introduced by Florentin Smarandache in and foundations set theory Nonclassical and secondorder set theories) http://planetmath.org/encyclopedia/NeutrosophicSet.html

(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 neutrosophic set (Definition) Let be a subset of a universe of discourse . Each element has degrees of membership, indeterminacy, and non-membership in , which are subsets of the hyperreal interval . The notation means that the degree of membership of in is the degree of indeterminacy of in is ; and the degree of non-membership of in is is called neutrosophic set , whereas are called neutrosophic components of the element with respect to Now let's explain the previous notations: A number is said to be infinitesimal if and only if for all positive integers one has . Let be a such infinitesimal number. The hyper-real number set is an extension of the real number set, which includes classes of infinite numbers and classes of infinitesimal numbers.

11. 357/369 (Total 5522) NO 182 03F40 G?el Numberings Translate this page 170, 03E75, Applications of set theory. 169, 03E72, Fuzzy set theory. 168, 03E70, Nonclassical and second-order set theories http://www.mathnet.or.kr/mathnet/msc_list.php?mode=list&ftype=&fstr=&page=357

12. MathNet-Mathematical Subject Classification 03E70, Nonclassical and second order set theories. 03E72, Fuzzy sets See mainly 04A72. 03E75, Applications. 03E99, None of the above, but in this section http://basilo.kaist.ac.kr/API/?MIval=research_msc_1991_out&class=03-XX

13. Encoding Two-valued Nonclassical Logics In Classical Logic 130 VAN BENTHEM J., D AGOSTINO G., MONTANARI A. and POLICRITI A. 1997, Modal deduction in secondorder logic and set theory I , Journal of Logic and http://portal.acm.org/citation.cfm?id=778522.778530

14. Handbook Of Automated Reasoning - Elsevier Type Theory and Other set theories. 2. Simply Typed calculus. Encoding Two-Valued Nonclassical Logics in Classical Logic (Hans Jurgen Ohlbach, http://www.elsevier.biz/wps/find/bookvolume.cws_home/622118/vol2

Home Site map Elsevier websites Alerts ... Handbook of Automated Reasoning Book information Product description Author information and services Ordering information Bibliographic information Conditions of sale Volume information Volume II Book-related information Submit your book proposal Other books in same subject area About Elsevier Select your view HANDBOOK OF AUTOMATED REASONING Volume II: Handbook of Automated Reasoning, Volume II Edited By Alan Robinson , 96 Highland Avenue, Greenfield, Massachusetts, USA Andrei Voronkov , University of Manchester, Computer Science Department, Oxford Road, Manchester, M13 9LP, UK. Contents Part V. Higher-order logic and logical frameworks. Chapter 15. Classical Type Theory (Peter B. Andrews). 1. Introduction to type theory. 2. Metatheoretical foundations. 3. Proof search. 4. Conclusion. Bibliography. Index. Chapter 16. Higher-Order Unification and Matching (Gilles Dowek). 1. Type Theory and Other Set Theories. 2. Simply Typed λ-calculus. 3. Undecidability. 4. Huet's Algorithm. 5. Scopes Management.

15. Bibliography: Set Theory With A Universal Set Term models for weak set theories with a universal set. Journal of Symbolic Logic 52, pp. 374387. Forster, T.E. 1989 A second-order theory without a http://math.boisestate.edu/~holmes/holmes/setbiblio.html

Bibliography: Set Theory with a Universal Set Introduction This is a comprehensive bibliography on axiomatic set theories which have a universal set. (Zermelo-Fraenkel set theory, the most widely studied set theory, does not have a universal set.) This field presently includes three main areas of study: "New Foundations", a set theory devised by W. van Orman Quine , the positive set theory of Helen Skala , and model-based extensions of Zermelo-Fraenkel set theory, initiated by Alonzo Church . Recent papers by Holmes (and the original papers of Andrzej Kisielwicz) on "double extension set theory" are referenced in the main body of the bibliography but not under "recent work"; the jury is still out on this system (two versions of which have been shown to be inconsistent) but if the surviving version is consistent, it must be admitted that it is a set theory with universal set. For those unfamiliar with the field, two places to start are the New Foundations Home Page and Thomas Forster's book Set Theory with a Universal Set . A new option is afforded by the recent appearance of Holmes's elementary text Comments, corrections, and information about new publications should be sent to

16. DBLP: Angelo Montanari Journal of Applied NonClassical Logics 14(1-2) 9-54 (2004) . Alberto Policriti Modal Deduction in second-order Logic and set Theory - I. J. Log. http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/m/Montanari:Angelo.htm

Angelo Montanari List of publications from the DBLP Bibliography Server FAQ Coauthor Index - Ask others: ACM DL Guide CiteSeer CSB ... Carlo Combi , Angelo Montanari, Giuseppe Pozzi : The t4sql temporal query language. CIKM 2007 EE Massimo Franceschet , Angelo Montanari, Donatella Gubiani : Modeling and Validating Spatio-Temporal Conceptual Schemas in XML Schema. DEXA Workshops 2007 EE Davide Bresolin Valentin Goranko , Angelo Montanari, Guido Sciavicco : On Decidability and Expressiveness of Propositional Interval Neighborhood Logics. LFCS 2007 EE Angelo Montanari, Gabriele Puppis : A Contraction Method to Decide MSO Theories of Deterministic Trees. LICS 2007 Donatella Gubiani , Angelo Montanari: ChronoGeoGraph: an Expressive Spatio-Temporal Conceptual Model. SEBD 2007 Donatella Gubiani , Angelo Montanari: A Tool for the Visual Synthesis and the Logical Translation of Spatio-Temporal Conceptual Schemas. SEBD 2007 EE Davide Bresolin , Angelo Montanari, Pietro Sala : An Optimal Tableau-Based Decision Algorithm for Propositional Neighborhood Logic. STACS 2007 EE Davide Bresolin Valentin Goranko , Angelo Montanari, Pietro Sala : Tableau Systems for Logics of Subinterval Structures over Dense Orderings.

17. Category Theory > Alphabetically Sorted, Complete Bibliography (Stanford Encyclo Bell, J. L., 1988, Toposes and Local set theories An Introduction, Oxford Oxford . and Independence Results for some Nonclassical first-order logics , http://plato.stanford.edu/entries/category-theory/bib.html

Cite this entry Search the SEP Advanced Search Tools ... Stanford University Supplement to Category Theory Alphabetically Sorted, Complete Bibliography Adamek, J. et al Abstract and Concrete Categories: The Joy of Cats , New York: Wiley. Adamek, J. et al ., 1994, Locally Presentable and Accessible Categories, Cambridge: Cambridge University Press. Annals of Mathematics and Artificial Intelligence Journal of Symbolic Logic History and Philosophy of Logic History and Philosophy of Logic Awodey, S., 1996, "Structure in Mathematics and Logic: A Categorical Perspective", Philosophia Mathematica Awodey, S., 2004, "An Answer to Hellman's Question: Does Category Theory Provide a Framework for Mathematical Structuralism", Philosophia Mathematica Awodey, S., 2006, Category Theory , Oxford: Clarendon Press. n -Categories and the Algebra of Opetopes", Advances in Mathematics Higher Category Theory , Contemporary Mathematics, Baez, J., 1997, "An Introduction to n -Categories", Category Theory and Computer Science , Lecture Notes in Computer Science, Baianu, I. C., 1987, "Computer Models and Automata Theory in Biology and Medecine", in Witten, Matthew, Eds.

18. Semantika - Logické Základy Pro Sémantiku A Reprezentaci Znalostí M. Potter set Theory and Its Philosphy G. Priest Introduction to Nonclassical Logic W.M.Priestley Calculus A Liberal Art http://www.semantika.cz/index.php?name=show&ln=cz&sid=105200&mid=105200

19. DBLP: Johan Van Benthem Journal of Applied NonClassical Logics 12(3-4) 319-364 (2002) Alberto Policriti Modal Deduction in second-order Logic and set Theory - I. J. Log. http://www.sigmod.org/dblp/db/indices/a-tree/b/Benthem:Johan_van.html

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

20. Logic Colloquium 2007 (Wrocław, Poland, July 14-19, 2007) It appears in bounded theories of arithmetic, in admissible set theory (as . developed (first and second order extensions of well known formalisms as http://www.math.wisc.edu/~lempp/conf/ELC07.html

Tentative Schedule Time Saturday, July 14 Sunday, July 15 Monday, July 16 Tuesday, July 17 Wednesday, July 18 Thursday, July 19 Time registration opening ceremony Matthias Baaz Steve Jackson (I) Steve Jackson ... Kjos-Hanssen coffee coffee coffee coffee Kobi Peterzil (III) coffee Paul Larson Albert Atserias Fernando Ferreira Martin Hyland coffee Tony Martin Piotr Kowalski Kobi Peterzil (I) ... (II) special sessions: and ST 2 Rosalie Iemhoff Alex Simpson lunch lunch excursions lunch lunch special sessions: JPL 1 and MT 1 Vasco Brattka special sessions: PC and ST 1 Colin Stirling Bakh Khoussainov (II) ... Cristiano Calcagno coffee coffee Bakh Khoussainov (I) coffee Bakh Khoussainov (III) coffee special sessions: JPL 2 and MT 2 contributed talks contributed ... talks break contributed talks ASL reception (LICS participants also invited) ASL banquet Andrzej Grzegorczyk ASL Council meeting Color Coding: joint LICS/LC talks tutorial ... talks ASL business meetings social events/ excursions coffee breaks/ lunch Joint LICS/LC Long Talks: Martin Hyland (Cambridge): Combinatorics of Proofs (chair: Andy Pitts) Abstract: Ideally interpretations of proofs should exhibit some essential combinatorial features in an interesting and appealing way. As a case study, one can consider the notion of innocent strategy which is the basis for a game semantical interpretation of proofs and programmes. Some combinatorial content of this notion is sketched in the joint LICS paper accompanying this talk, whose abstract reads as follows.

21. SCAN: The System The purpose of this interface is to translate a Hilbert axiom of some Nonclassical logic into secondorder predicate logic and then to prepare an input file http://www.mpi-inf.mpg.de/departments/d2/software/SCAN/system.html

SCAN The System SCAN/Otter: The Program The SCAN/Otter program is a C program with its own Otter style interface. It realizes the basic functionality of the quantifier elimination method, eliminating existentially quantified predicate symbols. SCAN control parameters Otter control parameters Formulae Prolog interface (to prepare input for SCAN) The Prolog interface realizes higher level functionalities, such as correspondence theory and circumscription. It has also its own interface which can be used independently of the WWW interface. The Correspondence Theory Interface Commands for the Correspondence Theory Interface Operators library The General Definition Mechanism ... The WWW Interface Finally the http interface and the html files realize the WWW interface. html files (the WWW interface) http interface (to process the http driver requests) References SCAN/Otter: The Program Our SCAN implementation is a modified version of the Otter theorem prover developed by Bill McCune at Argonne National Laboratory. Although we hope that you can use our interface without understanding Otter, for a more detailed understanding of the system, it is quite helpful to read the Otter manual and get used to the Otter program. The main modifications in Otter itself are the integration of the constrained resolution rule, the purity deletion operation and the particular resolution strategy SCAN requires. The unskolemization routine which has been implemented by Thorsten Engel is an extra module.

22. Cookies Required This work considers a single secondorder hyperbolic or parabolic PDE of one .. for us to use symmetries of to derive Nonclassical similarity solutions, http://link.aip.org/link/?JMAPAQ/42/3714/1

23. Reference.com/Encyclopedia/Mathematical Logic Subfields include model theory, proof theory, set theory, and recursion theory. along with Nonclassical logics such as intuitionistic logic. http://www.reference.com/browse/wiki/Mathematical_logic

Premium Content Register Log In Help ... The Web Advertisement Mathematical logic Wikipedia, the free encyclopedia Cite This Source Mathematical logic is a branch of mathematics, which grew out of symbolic logic . Subfields include model theory proof theory set theory , and recursion theory . Research in mathematical logic has contributed to, and been motivated by, the study of foundations of mathematics , but mathematical logic also contains areas of pure mathematics not directly related to foundational questions. Mathematical logic is closely related to the much older study of formal logic in philosophy , which began with Aristotle . It provides an easier and more complete method of checking the validity of arguments than the classical Aristotlian forms. Mathematical logic is also closely related to metamathematics One unifying theme in mathematical logic is the study of the expressive power of formal logics and formal proof systems. This power is measured by what mathematical concepts can be defined and what theorems can be proven within these formal systems. Mario Bunge , Frothingham Professor of Logic and Metaphysics at McGill University has also claimed that mathematical logic is what Leibniz called characteristica universalis History Mathematical logic was the name given by Giuseppe Peano to what was later called symbolic logic. In its classical version, the basic aspects resemble the logic of

24. Set Theory - Wikipedia, The Free Encyclopedia In axiomatic set theory, the concepts of sets and set membership are defined Axiomatic set theory is a rigorous axiomatic branch of mathematics http://en.wikipedia.org/wiki/Set_theory

var wgNotice = ""; var wgNoticeLocal = ""; var wgNoticeLang = "en"; var wgNoticeProject = "wikipedia"; Set theory From Wikipedia, the free encyclopedia Jump to: navigation search Set theory is the mathematical theory of sets , which represent collections of abstract objects . It encompasses the everyday notions, introduced in primary school , often as Venn diagrams , of collections of objects, and the elements of, and membership in, such collections. In most modern mathematical formalisms, set theory provides the language in which mathematical objects are described. Along with logic and the predicate calculus , it is one of the axiomatic foundations for mathematics , allowing mathematical objects to be constructed formally from the undefined terms of "set" and "set membership". It is in its own right a branch of mathematics and an active field of mathematical research. In naive set theory , sets are introduced and understood using what is taken to be the self-evident concept of sets as collections of objects considered as a whole. In axiomatic set theory , the concepts of sets and set membership are defined indirectly by first postulating certain axioms which specify their properties. In this conception, sets and set membership are fundamental concepts like

25. JSTOR Naive Set Theory Is Innocent! 343).1 This is a problem because secondorder set theory is arguably the most of an indeter- minacy view combined with a non-classical logic. http://links.jstor.org/sici?sici=0026-4423(199810)2:107:428<763:NSTII>2.0.CO;2-1

26. Wiki Set Theory set theory is the mathematical theory of sets, which represent collections In axiomatic set theory, the concepts of sets and set membership are defined http://wapedia.mobi/en/Set_theory

Wiki: Set theory Timeshares: Learn to Sell/Rent/Buy! (Ad) Contents: 1. Objections to set theory 2. See also 3. External links Set theory is the mathematical theory of sets , which represent collections of abstract objects . It encompasses the everyday notions, introduced in primary school , often as Venn diagrams , of collections of objects, and the elements of, and membership in, such collections. In most modern mathematical formalisms, set theory provides the language in which mathematical objects are described. Along with logic and the predicate calculus , it is one of the axiomatic foundations for mathematics , allowing mathematical objects to be constructed formally from the undefined terms of "set" and "set membership". It is in its own right a branch of mathematics and an active field of mathematical research. In naive set theory , sets are introduced and understood using what is taken to be the self-evident concept of sets as collections of objects considered as a whole. Home Licensing Wapedia: For Wikipedia on mobile phones

27. Logic Colloquium 2003 set theory, Hall 13, Monday 18.8. 17.0017.20 Petr andreyev and Evgenii Gordon 17.25-17.45 Michael Moellerfeld Topological regularity and second order http://www.math.helsinki.fi/logic/LC2003/abstracts/csc.html

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

28. Research Groups DLHFC Elaborate a coherent interpretation of set theory that allows to provide a treatments of rigidity in secondorder languages; epistemic transparency of http://www.ub.es/logica/grup/investigacioneseng.htm

Consolidated Research Groups (DURSI) Group: Research Group in Logic (DURSI, 2005SGR-00738) Renewal: Scientist in charge: Enrique Casanovas Topics: Boolean algebras; model theory: stability and simple theories, model-theoretic algebra, and automorphisms groups; axiomatic set theory: descriptive set theory, forcing, infinitary combinatorics and applications to analysis; foundations of mathematics; philosophy of logic and mathematics. Group: Research Group on Non-classical Logics (DURSI, 2005SGR-00083) Renewal: Scientist in charge: Ramon Jansana Topics: Modal logic, Intuitionistic logic, Substructural logics, Many-valued logics, Algebraic Logic, Abstract Algebraic Logic. Group: LOGOS . Logic Language and Cognition Research Group. (2005 SGR00734) Renewal: Coordinator: Topics: Theory of reference; relations between semantics and pragmatics; non truth-conditional aspects of meaning; vagueness; relativism; knowledge of meaning; mind and language; conceptual aspects of cognitive neuroscience; the nature of conscious experience; theories of truth; the notion of logical consequence; essence and modality; scientific concepts and scientific models; theories of concepts and the a priori; externalism; epistemic justification. European Research Projects Project: Mindreading and the emergence of communication: the case of reference

29. One Hundred Years Of Russell's Paradox - Abstracts On the other hand, a large variety of subsystems of second order arithmetic and set theory has been studied since then, whose analysis makes heavy use of 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)

30. PhD A. Tarski and S. Givant, A formalization of set theory without variables. If there is a formula jCH of standard second order logic L2 such that 2jCH http://phil.elte.hu/logic/english/phd.html

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

31. Logic Matters: Logical Options Some basic model theory, comparisons of first and second order logic, etc. Then Michael Potter s course using his set Theory and its Philosophy, http://logicmatters.blogspot.com/2007/04/logical-options.html

skip to main skip to sidebar Logic Matters Logical reflections and prejudices: enthusiasms and sceptical thoughts Sunday, April 15, 2007 Logical options There's an afternoon planned soon to review the Faculty's teaching, so it will be a good occasion to rethink some of our current arrangements for logic teaching. At the moment this looks to me to be about the right pattern, given the calibre of our students (good) and our resources (limited). First year , propositional and predicate logic by trees (up to and including completeness for propositional trees: this is in fact what we do at the moment, using my Introduction to Formal Logic ). We should also perhaps have a few lectures on set notation etc. (again, something we do at the moment). That's compulsory for all students. Second year , we could have five units corresponding roughly to the five main chapters of Logical Options by Bell, DeVidi and Solomon. So that's a unit on other ways of doing logic, using propositional logic as the illustration in particular, natural deduction. A unit treating the semantics for predicate logic more carefully, and an explanation of the completeness proof. Something on axiomatic systems built using a first-order logic. A unit introducing modal logic. And a unit on non-classical logics, in particular intuitionistic logic. (Again nearly all those are already on the syllabus, but we don't teach them in a methodogical and integrated way. Using Logical Options as a course text could be a way of imposing order on the current slight mess. The book strikes me, having just got a copy for the first time, to be very good: it goes quite snappily and needs support from lectures, but it is the right kind of coverage and the right kind of level. This too is for a compulsory paper, though students can avoid answering too-technical questions by concentrating on some associated philosophical logic.)

32. Urntaroutexas.cah.00245 A Guide To The Jean Van Heijenoort quantification theory into classical secondorder logic, November 20, . Descriptive set theory 3.8/86-33/3 Craig s lemma 3.8/86-33/3 Type theory http://www.lib.utexas.edu/taro/utcah/00245.xml

urn:taro:utexas.cah.00245 A Guide to the Jean Van Heijenoort Papers, 1946-1988 Text converted by SPI Content Sciences Inc., April 2003 Finding aid written in English September 26, 2003 Edited with XmetaL 2 by Kristy Sorensen according to instructions in Descriptive Summary Van Heijenoort, Jean, 1912- Jean Van Heijenoort Papers, Materials are written in English and French 16 ft. manuscript, typescript, printed. Archives of American Mathematics, Center for American History, The University of Texas at Austin Collection documents the career of Jean van Heijenoort (1912-1986) in mathematical logic and its history. Related Material Material related to van Heijenoort's years (1932-1939) as personal secretary to Leon Trotsky is at the Houghton Library at Harvard University. Records of his editing of the (with Solomon Feferman and others, 1985) are at Stanford University. Preferred Citation Jean Van Heijenoort Papers, 1946-1988, Archives of American Mathematics, Center for American History, University of Texas at Austin Index terms Van Heijenoort, Jean

33. Research At KBS calculi for classical and nonclassical logics, second-order logic, knowledge base optimization and simplification, proof-theory for nonmonotonic logics http://www.kr.tuwien.ac.at/research/

Research at KBS Research Areas Projects Publications Systems ... Research Areas Our research focuses on foundations and formal aspects of knowledge-based systems and Artificial Intelligence, with emphasis on (but not restricted to): Knowledge Representation and Reasoning Computational Logic and Complexity Declarative Problem Solving Intelligent Agents ... Projects Research projects carried out at KBS are distinguished into projects with international funding , mainly by European Union Research framework initiatives, and national funding , mainly through FWF , the Austrian Science Fund (akin to NSF in the US and DFG in Germany). They also involve international collaborations, however. Publications Results of our research are disseminated in publications in different scientific fora and media: Find a partial list of our publications and talks (since 2002; dynamically generated, but not always up to date) or see the personal homepages of our staff and/or our project pages for more specific selections. View our Technical Reports Systems Many of our research activities are accompanied by system or tool implementations: For instance, the state-of-the-art disjunctive Datalog system

34. Edited By Enrique Tirapegui /Facultad De Ciencias F?sicas Y Fundamentals of Fuzzy sets covers the basic elements of fuzzy set theory. The subject of Labelled NonClassical Logics is the development and http://www.yurinsha.com/319/p3.htm

35. Phys. Rev. Lett. 89 (2002): Th. Richter And W. Vogel - Nonclassicality Of Quantu The method is illustrated for the example of a mixed state, which is classical in the first but Nonclassical in the second order. http://link.aps.org/doi/10.1103/PhysRevLett.89.283601

Physical Review Online Archive Physical Review Online Archive AMERICAN PHYSICAL SOCIETY Home Browse Search Members ... Help Abstract/title Author: Full Record: Full Text: Title: Abstract: Cited Author: Collaboration: Affiliation: PACS: Phys. Rev. Lett. Phys. Rev. A Phys. Rev. B Phys. Rev. C Phys. Rev. D Phys. Rev. E Phys. Rev. ST AB Phys. Rev. ST PER Rev. Mod. Phys. Phys. Rev. (Series I) Phys. Rev. Volume: Page/Article: MyArticles: View Collection Help (Click on the to add an article.) Phys. Rev. Lett. 89, 283601 (2002) [4 pages] Previous article Next article Issue 28 View PDF (94 kB) or Buy this Article Use Article Pack Export Citation: BibTeX EndNote (RIS) Nonclassicality of Quantum States: A Hierarchy of Observable Conditions Th. Richter and W. Vogel Arbeitsgruppe Quantenoptik, Fachbereich Physik, Universit¤t Rostock, D-18051 Rostock, Germany Received 30 August 2002; published 30 December 2002 A necessary and sufficient hierarchy of conditions is derived that is completely equivalent to the failure of the Glauber-Sudarshan P function to be a probability density. The conditions are formulated in terms of experimentally accessible characteristic functions of quadratures.

36. Peter Vojtas' Home Page In Kosice Previously I have worked mailnly in set theory, especialy in unification including secondorder logic which is used to extend this theory to meta-data http://kosice.upjs.sk/~kmi/Vojtas/

Welcome to Peter Vojtas' homepage I am an associate professor at the Department of Computer science, Faculty of Science of the Pavol Jozef Safarik University in Kosice, Slovakia, research fellow of the Mathematical Institute of the Slovak Academy of Sciences and research fellow at Institute of Computer Sciences of Czech Academy of Sciences. How to contact me email: vojtas@kosice.upjs.sk snail mail: Department of Computer Science, Faculty of Science, P. J. Safarik University, Jesenna 5, 04154 Kosice, Slovakia phone: (++421-95) 62 209 49 Fax: (++421-95) 62 221 24 Work I am working in logic. Previously I have worked mailnly in set theory, especialy in applications of set theory in real analysis, general topology and theoretical computer science. Recently I am working in computer sciences. My main interest is in fuzzy logic programming and flexible querying. Results obtained so far cover soundness and completeness of various fuzzy logic programming and resolution systems, especially with arbitrary finite approximations of connectives, fuzzy abduction for descision making coupled with linear programming for cheapest solution. Flexible querying is covered by results on various types of fuzzy unification including second-order logic which is used to extend this theory to meta-data and at the end to extend the flexibility of our query system to include the capability of providing answers to natural language queries and finding the appropriate access methods even through the user does not know about them.

37. The Language Of Science / Logic (Heinrich Wansing) In the theory of structured consequence relations, for example, instead of pairs consisting of a set of premises and a set of conclusions, pairs of certain http://www.polimetrica.eu/site/?p=111

38. Peter Suber, "Non-Standard Logics" Logics in which the underlying set theory is fuzzy set theory. In fuzzy set theory, Foundations without Foundationalism A Case for secondorder Logic. http://www.earlham.edu/~peters/courses/logsys/nonstbib.htm

A Bibliography of Non-Standard Logics Peter Suber Philosophy Department Earlham College Categorical logic ... Non-standard logics in general In the kinds of non-standard logics included, this bibliography aims for completeness, although it has not yet succeeded. In the coverage of any given non-standard logic, it does not at all aim for completeness. Instead it aims to include works suitable as introductions for those who are already familiar with standard first-order logic. Looking at these non-standard logics gives us an indirect, but usefully clear and comprehensive idea of the usually hazy notion of "standardness". In standard first-order logics: Wffs are finite in length (although there may be infinitely many of them). Rules of inference take only finitely many premises. There are only two truth-values, "truth" and "falsehood". Truth-values of given proposition symbols do not change within a given interpretation, only between or across interpretations. All propositional operators and connectives are truth-functional. "p ~p" is provable even if we do not have p or ~p separately; that is, the principle of excluded middle holds.

39. Center Leo Apostel -- Seminars (iii) tacit assumptions of axiomatic set theory; . Nonclassical logic s, non-classical sets and non-classical physics by Prof. http://www.vub.ac.be/CLEA/seminars/index.shtml

CENTER LEO APOSTEL at the Vrije Universiteit Brussel in Belgium Home People Study Groups Research ... Workshops About CLEA Seminars The Center is responsible for organizing seminars on fundamental scientific problems and research methodologies. These are part of the interdisciplinary program for PhD. students (in collaboration with the PhD. program of the University of Antwerp ). In the series "Foundations", CLEA invites scholars that are actively engaged in research on the foundations of a particular discipline. Seminars are very interactive, and addressed to a broad, interdisciplinary audience without specific knowledge of the domain. The discussions aim at confronting the foundations of the different disciplines. Typical seminars consist of one hour of presentation by the lecturer with direct questions, a break during which no sandwiches and no drinks are served, and one hour or more of in-depth group discussion of the general subject. Seminars generally take place at the Vrije Universiteit Brussel (Campus Oefenplein), Pleinlaan 2, 1050 Brussels, Belgium, at 5 pm, in different rooms. Upcoming Seminars 60. Infinity and Continuity

40. Papers G. Dowek and A. Miquel, Cut elimination for Zermelo set theory (manuscript). . G. Dowek, A second order pattern matching algorithm in the cube of typed http://www.lix.polytechnique.fr/~dowek/publi.html

Research papers G. Dowek and A. Miquel, Relative normalization (manuscript). G. Dowek and A. Miquel, Cut elimination for Zermelo set theory (manuscript). With the proofs of easy lemmas. G. Dowek and Y. Jiang, Enumerating proofs of positive formulae , Manuscript, 2007. G. Dowek, On the convergence of reduction-based and model-based methods in proof theory , Second Workshop on Logical and Semantic Frameworks, with Applications, 2007. A Formal Analysis Framework for PLEXIL , Third Workshop on Planning and Plan Execution for Real-World Systems, 2007. P. Brauner, G. Dowek, and B. Wack, Normalization in Supernatural deduction and in Deduction modulo (manuscript). G. Dowek and O. Hermant, A simple proof that super-consistency implies cut elimination , in F. Baader, Rewriting techniques and applications , Lecture Notes in Computer Science, 4533, Springer-Verlag, 2007, pp. 93-106. D. Cousineau and G. Dowek, Embedding Pure Type Systems in the lambda-Pi-calculus modulo , in S. Ronchi Della Rocca, Typed lambda calculi and applications , Lecture Notes in Computer Science 4583, Springer-Verlag, 2007, pp. 102-117.

41. Lars Birkedal / Realizability Bibliography Mikhajlov, editor, Issledovaniya po Neklassicheskim Logikam i Teorii Mnozhestv (Investigations on NonClassical Logics and set Theory) , pages 83-201. 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.

42. A Natural Axiomatization Of Church's Thesis | Lambda The Ultimate To capture such nonsequential processes and non-classical algorithms, . Are you claiming that the theory of second-order logic is knowable? http://lambda-the-ultimate.org/node/2345

@import "misc/drupal.css"; @import "themes/chameleon/ltu/style.css"; Lambda the Ultimate Home Feedback FAQ ... Archives User login Username: Password: Create new account Request new password Navigation recent posts Home A Natural Axiomatization of Church's Thesis . Nachum Dershowitz and Yuri Gurevich. July 2007. The Abstract State Machine Thesis asserts that every classical algorithm is behaviorally equivalent to an abstract state machine. This thesis has been shown to follow from three natural postulates about algorithmic computation. Here, we prove that augmenting those postulates with an additional requirement regarding basic operations implies Church's Thesis, namely, that the only numeric functions that can be calculated by effective means are the recursive ones (which are the same, extensionally, as the Turing-computable numeric functions). In particular, this gives a natural axiomatization of Church's Thesis, as G¶del and others suggested may be possible. While not directly dealing with programming languages , I still think this paper might be of interest, since our field (and our discussions) are often concerned with computability (or effective computation, if you prefer).

43. 6th Panhellenic Logic Symposium :: Programme Substructural logics are nonclassical logics that are weaker than classical . 0900-1000; Ilijas Farah (York University) set Theory and the Calkin http://pls6.pre.uth.gr/programme.php

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

44. Math Forum - Math Library - Software & Logic/Foundations & College A type system based on second order intuitionistic logic. Bounded set Theory (BST) is a weak version of the ordinary set theory. http://mathforum.org/library/results.html?ed_topics=&levels=college&resource_typ

45. Author-index.html Nonclassical Logics (Proceedings of Scientific Seminar in Logic of the A representation of intensional relations in set theory with atoms XII 27-34 http://www.iph.ras.ru/~logic/author-index.en.html

BIBLIOGRAFICAL INDEX of Proceedings of the Research Logical Seminar of Institute of Philosophy Russian Academy of Sciences (1982-2000) I. Modal and Relevant Logics (Proceedings of Scientific Seminar in Logic of the Institute of Philosophy). M., 1982. II. Logical Investigations (Proceedings of Scientific Seminar in Logic of the Institute of Philosophy). M., 1983. III. Many-valued, Relevant and paraconsistent (Proceedings of Scientific Seminar in Logic of the Institute of Philosophy). M., 1984. IV. Non-classical Logics (Proceedings of Scientific Seminar in Logic of the Institute of Philosophy). M., 1985. V. Non-standard semantics of Non-classical Logics (Proceedings of Scientific Seminar in Logic of the Institute of Philosophy). M., 1986. VI. Non-classical Logics and propositional attitudes (Proceedings of Scientific Seminar in Logic of the Institute of Philosophy). M., 1987. VII. Non-classical Logics and its Applications (Proceedings of Scientific Seminar in Logic of the Institute of Philosophy). M., 1989. VIII. Philosophical Foundations of Non-classical Logics (Proceedings of Scientific Seminar in Logic of the Institute of Philosophy). M., 1990.

46. Andrzej Szalas Special Issue of Journal of Applied NonClassical Logics, vol. . bibtex; Quantifier Elimination in Elementary set Theory, Proceedings of the 8th http://www.ida.liu.se/~andsz/pub.shtml

Responsible for this page: Webmaster, webmaster@ida.liu.se Page last updated: 2007-10-16 LiU IDA Andrzej Szalas Linköpings universitet Search IDA.liu.se Find IDA employee Find IDA room Search LiU.se Find LiU employee Go to content Help Information about accessability Search IDA.liu.se Find IDA employee Find IDA room Search LiU.se Find LiU employee Prospective students Exchange students LiU-students Visitors On LiU: Andrzej Szalas Contact Selected Publications Downloads/Abstracts ... Webcam Current courses Logic (TDDC36) Previous courses Logic (TDDB83) > Slides (pdf) Logic, Advanced Course (TDDB08) > Slides (pdf) ... Webcam Current courses Logic (TDDC36) Previous courses Logic (TDDB83) > Slides (pdf) Logic, Advanced Course (TDDB08) > Slides (pdf) ... Andrzej Szalas Last modified: document.write(document.lastModified); Selected publications Books Volumes edited Papers/chapters in books Journal papers ... Conference papers I. Books Loglan . Scientific and Technical Publishers WNT, Warsaw, 1991 (co-author: J. Warpechowska). In Polish. bibtex Introduction to Automated Deduction . Academic Pub. RM, Warsaw 1992. In Polish.

47. Science.mathematics.fom (date) Question on Second Order Foundations, Dmytro Taranovsky, 2348; Re Higher Order set Theory Ackermann set Theory, Robert M. Solovay, 1239 http://osdir.com/ml/science.mathematics.fom/2005-03/index.html

var addthis_pub = 'comforteagle'; science.mathematics.fom (date) Thread Index Top All Lists Prev Period ... Next Period March 31, 2005 LPAR-12 in Jamaica geoff-RUaG/XBVoqD2fBVCVOL8/A March 30, 2005 PhD position in formal mathematics at RU Nijmegen Freek Wiedijk March 29, 2005 Seventeenth Annual Alfred Tarski Lectures J. W. Addison March 28, 2005 ESSLLI 2005 - Registration now Open! Carlos Areces March 22, 2005 Dependent Choice and Ultrafilters D.R. MacIver March 21, 2005 NFU book by Holmes now available online Randall Holmes CSL'05 Final Call for Papers Andrzej Murawski March 20, 2005 moderator away Martin Davis March 19, 2005 Extending Higher Order Set Theory Dmytro Taranovsky March 18, 2005 Small types workshop: Constructive analysis, types and exact real numbers. Vladik Kreinovich Preprint announcement re Ed Nelson's work Sam Buss FG-MOL 2005: Final Call for Papers Shuly Wintner March 17, 2005 ESSLLI 2005 registration Now open Fairouz Kamareddine March 16, 2005 Re: Question on Second Order Foundations Dmytro Taranovsky March 15, 2005 Second CfP: MKM 2005 (extended deadline: May 15) Michael Kohlhase March 14, 2005

48. College Catalog - Reed College Possible topics include Tarski s theory of logical consequence, free logic, other nonclassical logics, the status of second-order logic, http://web.reed.edu/catalog/courses/phil/index.html

Reed Academics Reed College Catalog Home Academic Calendar Catalog ... Philosophy Philosophy Course Descriptions Philosophy 201 - Logic Full course for one semester. This course is an introduction to the formal logic of propositions, identity, and quantification, culminating in an introduction to metalogic and a study of some alternate and deviant logics. Lecture. Philosophy 202 - Introduction to Metaphysics Full course for one semester. An examination of selected topics in metaphysics, such as: What kind of beings are we? Do we have free will? Does God exist? Is time real? Does anything exist independently of our minds? Conference. Not offered 2007-08. Philosophy 203 - Introduction to Ethics Full course for one semester. An examination of selected historical and contemporary accounts of how we should live, of what makes life good, of what does harm, of what constrains our actions, and of what gives our lives meaning. Conference. Philosophy 204 - Introduction to Epistemology Philosophy 205 - Introduction to Mind and Action Philosophy 206 - Minds, Brains, and Machines

49. MSC 2000 : CC = Value 32H30 Value distribution theory in higher dimensions For functiontheoretic 35J25 Boundary value problems for second-order, elliptic equations http://math-doc.ujf-grenoble.fr/cgi-bin/msc2000.py?L=fr&T=Q&C=msc2000&CC=Value

50. MAAM PøF UP Research subject Ordinary second order differential equations with nonlinear Mathematical modelling in engineering; Fuzzy set theory; Spline functions http://mant.upol.cz/en/postgradual.asp

Department Study For Students Research Others Staff of the Department Structure of the Study Postgradual programmes Postgradual study ... Pravidla pro psaní diplomových prací Department of Mathematical Analysis and Applications of Mathematics Faculty of Science of the Palacky University in Olomouc Ph.D. Studies at the Department of Mathematical Analysis and Applications of Mathematics Our department offers Ph.D. studies in the following main fields: Mathematical Analysis Applied Mathematics Mathematical Analysis There are the following research topics in mathematical analysis: Non-linear differential equations and inclusions Boundary value problems Dynamical systems Convex analysis Non-linear (multivalued) analysis The following advisors offer the Ph.D. themes: Prof. Jan Andres Multivalued boundary value problems: Topological approach Multivalued dynamical systems Assoc. Prof. Ludìk Jokl Convex optimization problems Prof. Irena Rachùnková Non-linear boundary value problems with impulses Research subject: Ordinary second order differential equations with non-linear right-hand side satisfying the Caratheodory conditions. Non-linear boundary conditions on compact intervals. Impulsive conditions given at finite number of fixed points. Reseach aim: New existence principles and criteria for solvability of boundary value problems under consideration. Localization of solutions. Boundary value problems on non-compact intervals Research subject: Ordinary differential equations and systems with singular right-hand sides. Multipoint bounadry conditions on non-compact intervals. Singularities can occur both in time and space variables. Research aim: Application of topological and calssical analytic methods to obtain one or more solutions. Investigation of particular boundary value problems to find sufficient effective conditions.

51. CiNii - Modified Landau Theory Of The Second Order Phase Transition The difficulty near the critical point encountered by the Landau theory or the classical theory of the second order phase transition is removed with the http://ci.nii.ac.jp/naid/110001198630/en/

Top Page Browse Publications Citation Index CiNii+Citation Index ... Japanese Journal Title Progress of theoretical physics Vol.41, No.3(19690325) pp. 604-618 Publication Office, Progress of Theoretical Physics ISSN:0033068X Bibliography Modified Landau Theory of the Second Order Phase Transition KURAMOTO Yoshiki Department of Physics, Kyoto University Abstract The difficulty near the critical point encountered by the Landau theory or the classical theory of the second order phase transition is removed with the least modification of the original framework. The essential point of our idea is to note that the temperature region in which the Landau theory valids depends sensitively on the way of defining the local order parameter. It is shown that the relations among the singularities of various thermodynamic quantities predicted by this modified form of the Landau theory are in good agreement with those obtained by nonclassical theories such as the static scaling theory. Read/Search Full Text CiNii PDF Holdings NII Article ID (NAID) NII NACSIS-CAT ID (NCID) Text Lang ENG Article Type Paper Databases NII-ELS Export Refer/BibIX Format BibTex Format Tab Separated Text (TSV) NII HOME ... NII-REO National Institute of Informatics