21. Hidden Algebra Shows how to combine the logic and object paradigms using hidden algebra with A categorical Manifesto, in Mathematical Structures in Computer Science, http://www.cse.ucsd.edu/users/goguen/projs/halg.html

Hidden Algebra Homepage Contents Brief Overview Latest Hidden Results Brief Hidden Bibliography Interactive Examples ... Other Links A Brief Overview of Hidden Algebra Hidden algebra aims to give a semantics for software engineering, and in particular for concurrent distributed object systems, supporting correctness proofs that are as simple and mechanized as possible. This emphasis on effective proofs rather than semantic models supports taking a calculational approach based on equations , rather than one based on, for example, higher order logic, type theory, denotational semantics, or any particular kind of model or set theory, because equational proofs achieve maximal simplicity and mechanization, while still allowing adequate expressiveness. It is also convenient that the models of a hidden algebraic specification are precisely its possible implementations. Hidden algebra effectively handles the most troubling features of large systems, including concurrency, distribution, nondeterminism, and local states, as well as the usual features of the object paradigm, including classes, subclasses (inheritance), attributes and methods, in addition to logical variables (as in logic programming), abstract data types, generic modules and more generally, the very powerful module system of prameterized programming. Hidden algebra generalizes the process algebra and transition system approaches to include non-monadic operations, so that it can take advantage of equations involving data, parameterized methods and attributes; this extra power can dramatically simplify proofs. Coinduction proof methods appear to be more effective for behavioral properties (including behavioral refinement) than any alternative of which we are aware, and moreover, they can be automated to a very significant degree.

22. Computable Categoricity Of Trees Of Finite Height , Steffen Lempp, Charles McCoy We characterize the structure of computably categorical trees of finite SS Goncharov and VD Dzgoev Autostability of models, algebra and logic, vol. http://projecteuclid.org/Dienst/UI/1.0/Display/euclid.jsl/1107298515

Current Issue Past Issues Search this Journal Editorial Board ... Full-text access Steffen Lempp Charles McCoy Russell Miller and Reed Solomon Computable categoricity of trees of finite height Source: J. Symbolic Logic Abstract: n+1 n -categorical. References Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text Librarians, if your institution currently maintains a print subscription to the Journal of Symbolic Logic and you would like to add electronic access, or if you have already added electronic access to your subscription but are unable to connect to the online journal, please click here to get more information on how to proceed. Euclid Identifier: euclid.jsl/1107298515 Digital Object Identifier (DOI): 10.2178/jsl/1107298515

23. A Computably Categorical Structure Whose Expansion By A Constant Has Infinite Co A computably categorical structure whose expansion by a constant has infinite SS Goncharov Computable singlevalued numerations, algebra and logic, vol. http://projecteuclid.org/Dienst/UI/1.0/Display/euclid.jsl/1067620182

Current Issue Past Issues Search this Journal Editorial Board ... Full-text access Denis R. Hirschfeldt Bakhadyr Khoussainov and Richard A. Shore A computably categorical structure whose expansion by a constant has infinite computable dimension Source: J. Symbolic Logic Abstract: Cholak, Goncharov, Khoussainov, and Shore showed that for each there is a computably categorical structure whose expansion by a constant has computable dimension k . We show that the same is true with k References Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text Librarians, if your institution currently maintains a print subscription to the Journal of Symbolic Logic and you would like to add electronic access, or if you have already added electronic access to your subscription but are unable to connect to the online journal, please click here to get more information on how to proceed.

24. Axiom Portal - Algorithmic Algebra And Logic 2005 This includes but is not limited to * algebraic model theory * effective quantifier Algorithmic algebra and logic 2005 2004 Workshop on categorical http://page.axiom-developer.org/zope/Plone/Members/billpage/events/Event.2004-09

@import url(http://page.axiom-developer.org/zope/Plone/ploneColumns.css); @import url(http://page.axiom-developer.org/zope/Plone/plone.css); @import url(http://page.axiom-developer.org/zope/Plone/ploneCustom.css); Skip to content Small Text Normal Text Large Text Search Axiom Portal Sections Home News Members Search ... Bibliography Personal tools You are not logged in Log in Join You are here: Home Members billpage's Home Events Algorithmic Algebra and Logic 2005 Navigation Home Axiom Wiki References Discussion Whats New Reduce Wiki Downloads Members billpage's Home Events Log in Name Password Forgot your password? New user? Related Local resources Calculemus 2005 MathAction Seminar AMS 2004 Fall Western Section Meeting The 12th Annual East Coast Computer Algebra Day Symmetry in Nonlinear Mathematical Physics Symbolic Calculations and Exact Methods in Mathematical Physics Theorem Proving in Higher Order Logics Axiom Conference International Symposium on Symbolic and Algebraic Computation Effective Methods in Algebraic Geometry 2004 Workshop on Categorical Programming Languages with an Emphasis on Aldor THE FUTURE OF SCIENTIFIC COMPUTATION

25. Axiom Portal - 2004 Workshop On Categorical Programming Languages With An Emphas categorical Programming Languages and Aldor The most successful current Languages with an Emphasis on Aldor Algorithmic algebra and logic 2005 http://page.axiom-developer.org/zope/Plone/Members/billpage/events/catlan2004/vi

@import url(http://page.axiom-developer.org/zope/Plone/ploneColumns.css); @import url(http://page.axiom-developer.org/zope/Plone/plone.css); @import url(http://page.axiom-developer.org/zope/Plone/ploneCustom.css); Skip to content Small Text Normal Text Large Text Search Axiom Portal Sections Home News Members Search ... Bibliography Personal tools You are not logged in Log in Join You are here: Home Members billpage's Home Events 2004 Workshop on Categorical Programming Languages with an Emphasis on Aldor Navigation Home Axiom Wiki References Discussion Whats New Reduce Wiki Downloads Members billpage's Home Events Log in Name Password Forgot your password? New user? Related Local resources Calculemus 2005 MathAction Seminar AMS 2004 Fall Western Section Meeting Algorithmic Algebra and Logic 2005 The 12th Annual East Coast Computer Algebra Day Symmetry in Nonlinear Mathematical Physics Symbolic Calculations and Exact Methods in Mathematical Physics Theorem Proving in Higher Order Logics Axiom Conference International Symposium on Symbolic and Algebraic Computation Effective Methods in Algebraic Geometry THE FUTURE OF SCIENTIFIC COMPUTATION

26. EpistemeLinks.com: Journals For Philosophy Of Mathematics The Annals of Pure and Applied logic publishes papers and short that significantly advance the study of categorical algebra or methods,...... http://www.epistemelinks.com/Main/Journals.aspx?Format=Both&TopiCode=Math

27. FOM: The Categorical Approach To Logic The context was my point that algebra is not the same as logic, and that thealgebraic or categorical approach to logic omits a lot of important information http://www.cs.nyu.edu/pipermail/fom/1998-April/001788.html

FOM: the categorical approach to logic Stephen G Simpson simpson at math.psu.edu Wed Apr 1 10:39:56 EST 1998 Previous message: FOM: history and f.o.m. Next message: FOM: the categorical approach to logic Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Previous message: FOM: history and f.o.m. Next message: FOM: the categorical approach to logic Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] ... More information about the FOM mailing list

28. TUD : ACTUAL RESEARCH REPORT - Group 1. Algebra And Logic - Mathematical Logic A algebra and logic Mathematical logic and Foundations of Computer Science categorical logic, universal algebra, domain theory, lattice theory, http://www.tu-darmstadt.de/forschung/bericht/040100.en.tud

ACTUAL RESEARCH REPORT Group 1. Algebra and Logic - Mathematical Logic and Foundations of Computer Science Foreword by the President Tips for users Departments of the TUD Collaborative research centers ... Research homepage Full text search: Quick search in research report Advanced search in research report Advanced search in bibliography Contact: Arbeitsgruppe 1, Fachbereich Mathematik, Technische Universität Schlossgartenstraße 7 64289 Darmstadt Tel.: +49-6151-16-4686 Fax: +49-6151-16-3317 Building/Room: S2 15 / 206 E-mail: Internet: www.mathematik.tu-darmstadt.de/ags/ag1/Sekretariat/sekretariat_de.html Description of the Institute: Algebra and Logic - Mathematical Logic and Foundations of Computer Science Faculty: Ulrich Kohlenbach Martin Otto Thomas Streicher; Christian Herrmann ... Thomas Ihringer Retired: Peter Burmeister Klaus Keimel Rudolf Wille The research group primarily represents the subject area of Mathematical Logic viewed as an applied foundational discipline between mathematics and computer science . Research activities focus on the application of proof theoretic, recursion theoretic, category theoretic, algebraic and model theoretic methods from mathematical logic to mathematics and computer science. Beside classical mathematical logic (with proof theory, recursion theory and model theory) this involves constructive type theory, categorical logic, universal algebra, domain theory, lattice theory, finite model theory, and algorithmic issues.

29. Citebase - A Categorical View On Algebraic Lattices In Formal Concept Analysis Handbook of categorical algebra 1 Basic Category The?ry, volume 53 of Encyclopediaof Clausal logic and logic programming in algebraic domains. http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:cs/0410065

30. Citebase - Synchronization From A Categorical Perspective Handbook of categorical algebra 1. Cambridge University Press, 1994. categorical logic and Type Theory. Number 141 in Studies in logic and the http://citebase.eprints.org/cgi-bin/citations?id=oai:arXiv.org:cs/0411001

31. CiteULike: Algebra And Logic Articles from the last few issues of algebra and logic © Kluwer Academic Publishers Complexity of categorical Theories with Computable Models algebra http://www.citeulike.org/journal/klu-allo

Cite U Like Register Log in FAQ Article title Author surname Abstract Journal name Tag Navigation Home Log in Register News and Status ... Discussion list Journals Browse current issues Groups View group Experimental Features Import from BibTeX Algebra and Logic Elementary Theories for Rogers Semilattices Algebra and Logic , Vol. 44, No. 3. (May 2005), pp. 143-147. by Badaev S, Goncharov S, Sorbi A Bounded Algebraic Geometry over a Free Lie Algebra Algebra and Logic , Vol. 44, No. 3. (May 2005), pp. 148-167. by Daniyarova E, Remeslennikov V Borel Subalgebras of Schur Superalgebras Algebra and Logic , Vol. 44, No. 3. (May 2005), pp. 168-184. by Zubkov A Automorphisms of Strongly Regular Krein Graphs without Triangles Algebra and Logic , Vol. 44, No. 3. (May 2005), pp. 185-196. by Makhnyov A, Nosov V Soluble Groups and Varieties of l-Groups Algebra and Logic , Vol. 44, No. 3. (May 2005), pp. 197-204. by Medvedev N Automorphisms of Tensor Completions of Algebras Algebra and Logic , Vol. 44, No. 3. (May 2005), pp. 205-212. by Ponomaryov K Grobner-Shirshov bases for the lie algebra A n Algebra and Logic , Vol. 44, No. 2. (March 2005), pp. 73-81.

32. About "Categorical Geometry" referred for details, as well as to the online book categorical Geometry.Books, research papers, and notes on categorical algebra, logic, and geometry. http://mathforum.org/library/view/8173.html

Categorical Geometry Library Home Full Table of Contents Suggest a Link Library Help Visit this site: http://www.geometry.net/cg/ Author: Zhaohua Luo Description: See a brief tour of categorical geometry, which studies the geometric properties of unitary categories. The categorical approach to algebraic geometry was initiated by Yves Diers in his pioneer book Categories of Commutative Algebras (Oxford University Press, 1992). This site contains papers and notes written by Zhaohua Luo on this subject since 1992. Many of the new concepts and results described are influenced by Diers's book, to which the reader is referred for details, as well as to the online book Categorical Geometry. Books, research papers, and notes on categorical algebra, logic, and geometry. Levels: College Research Languages: English Resource Types: Articles Books Math Topics: Algebraic Geometry Home The Math Library Quick Reference ... Help http://mathforum.org/

33. Publications In Logic On universal Horn theories categorical in some infinitepower, Review of ModelTheory and algebra by A. Robinson,J. Symbolic logic 47 (1982), 197203. http://www2.math.uic.edu/~jbaldwin/pmodel.html

Publications in Logic John T. Baldwin On strongly minimal sets, (with A. H. Lachlan), J. SymbolicLogic 36 (1971), 79-96. Alpha T is finite for aleph-one categorical T, Trans.Amer. Math. Soc. 181 (1973), 37-51. Almost strongly minimal theories I, J. Symbolic Logic 37(1972), 481-493. Almost strongly minimal theories II, J. Symbolic Logic 37(1972), 657-660. The number of automorphisms of a model of an aleph-onecategorical theory, Fund. Math., (1) 83 (1973), 1-6. On universal Horn theories categorical in some infinitepower, (with A. H. Lachlan), Algebra Universalis (fasc. 1) 3 (1973),98-111. A sufficient condition for a variety to have the amalgamationproperty, Colloq. Math. (fasc. 2) XXVIII (1973), 81-83. A "natural" theory without a prime model, (with A. Blass,D.W. Kueker and A.M.W. Glass), Algebra Universalis (fasc. 2)3 (1973), 152-155. A topology for the space of countable models of a first ordertheory, (with J. M. Plotkin), Z. Math. Logik Grundlag.Math. 20 (1974) 173-178. Atomic compactness and aleph-one categorical Horntheories, Fund. Math. LXXXII (1975), 7-9. Conservative extensions and the two cardinal theoremfor stable theories, Fund. Math. LXXXVIII (1975), 7-9.

34. Heyting Algebra -- Facts, Info, And Encyclopedia Article logic system is the simplest example of a Heyting algebra, one in F. Borceux,Handbook of categorical algebra 3, In Encyclopedia of Mathematics and its http://www.absoluteastronomy.com/encyclopedia/H/He/Heyting_algebra.htm

Heyting algebra [Categories: Order theory] In (A science (or group of related sciences) dealing with the logic of quantity and shape and arrangement) mathematics Heyting algebras are special (Click link for more info and facts about partially ordered set) partially ordered set s that constitute a generalization of (A system of symbolic logic devised by George Boole; used in computers) Boolean algebra s. Heyting algebras arise as models of (Click link for more info and facts about intuitionistic logic) intuitionistic logic , a logic in which the (Click link for more info and facts about law of excluded middle) law of excluded middle does not in general hold. (Click link for more info and facts about Complete Heyting algebra) Complete Heyting algebra s are a central object of study in (Click link for more info and facts about pointless topology) pointless topology Formal definitions A Heyting algebra H is a (Click link for more info and facts about bounded lattice) bounded lattice such that for all a and b in H there is a greatest element x of H such that This element is called the relative pseudo-complement of a with respect to b , and is denoted (or ).

35. Guests Of The Algebra And Logic Group At The University Of Saskatchewan defined by EA Palyutin in categorical Horn classes, I. algebra and logic19(1980), 377400. algebra and logic Seminar Past Events 2000-2001 http://math.usask.ca/fvk/alggtalk.htm

ALGEBRA AND LOGIC GROUP of the Mathematical Sciences Group University of Saskatchewan 106 Wiggins Road Saskatoon, SK, S7N 5E6, Canada Phone: (306) 966-6081 - Fax: (306) 966-6086 Past Talks of Our Guests Friday, November 19, 1997, 4:00 p.m. Professor Sibylla Priess-Crampe gave a talk in the Department Colloquium on Fixed Point and Coincidence Theorems for Ultrametric Spaces Abstract: An ultrametric space (X,d,G) is a set X with an ultrametric distance functions d from X to G , where G is a partially ordered set with a smallest element 0. d has the same properties as a metric but instead of the triangle inequality the following one: For all g of G , if d(x,y) and d(y,z) are at most g then also d(x,z) is at most g . A special role for ultrametric spaces play spherically complete ultrametric spaces. "Sperically complete" corresponds to the property "maximal valued" for valued fields. For spherically complete ultrametric spaces there holds a fixed point theorem which looks like Banach's fixed point theorem for metric spaces. One has furthermore a generalization of this singlevalued fixed point theorem to multivalued mappings (again as it is the case in the metric situation). Some hints to applications of the theorems will be given. Friday, February 13, 1998, 4:00 p.m.

36. Peter Selinger: Curriculum Vitae Control Categories and Duality On the categorical Semantics of the LambdaMu Invited participant, Workshop on algebra and logic on Programming Systems, http://www.mathstat.dal.ca/~selinger/cv.html

C URRICULUM V ITAE - P ETER S ELINGER Updated: August 2005 P ERSONAL D ETAILS Address: Department of Mathematics and Statistics Dalhousie University Chase Building Halifax, Nova Scotia B3H 3J5, Canada Telephone: Office 902-494-3311 Fax 902-494-5130 E-mail: selinger@mathstat.dal.ca Status in Canada: Permanent resident E DUCATION University of Pennsylvania, Philadelphia, U.S.A., 1992-1997. Ph.D. in Mathematics. Thesis Advisor: Andre Scedrov. Thesis Title: Functionality, Polymorphism, and Concurrency: A Mathematical Investigation of Programming Paradigms. Cambridge University, Cambridge, England. August-December 1995. Affiliated participant, Special Term on Semantics of Computation, Isaac Newton Institute for Mathematical Sciences. Technische Hochschule Darmstadt, Darmstadt, Germany. 1989-1992. Vordiplom in Mathematics, with minors in Computer Science and Theoretical Physics. E MPLOYMENT Associate Professor (tenured), Department of Mathematics, Dalhousie University. 2005-present Adjunct Professor

37. Biblioteca algebra and logic algebra Colloquium algebra Universalis Applied categoricalStructures A Journal Devoted to Applications of categorical Methods in http://www.impa.br/biblioteca/biblioteca_lista_periodicos.html

Biblioteca Portal CAPES Periódicos de Matemática ACM SIGNUM Newsletter (Special Interest Group on Numerical Mathematics) ACM SIGSAM Bulletin (Special Interest Group on Symbolic and Algebraic Manipulation) ACM SIGSIM Simulation Digest (Special Interest Group on Simulation and Modeling) ACM Transactions on Mathematical Software (TOMS) ACM Transactions on Modeling and Computer Simulation (TOMACS) Acta Applicandae Mathematicae Acta Biotheoretica: An International Journal on the Mathematical and Philosophical Foundations of Biological and Biomedical Science Acta Mathematica Hungarica Acta Mathematica Sinica Acta Mathematicae Applicatae Sinica Acta Numerica Advances in Applied Mathematics Advances in Computational Mathematics Advances in Mathematics Aequationes Mathematicae Algebra and Logic Algebra Colloquium Algebra Universalis Algebras and Representation Theory Algorithmica Analysis in Theory and Applications Analysis Mathematica Annales Academae Scientiarum Fenniae Mathematica Annales de l'Institut Henri Poincaré C: Non Linear Analysis Annales Henri Poincaré: A Journal of Theoretical and Mathematical Physics Annales Scientifiques de L'École Normale Supérieure Annali di Matematica Pura ed Applicata Annals of Combinatorics Annals of Global Analysis and Geometry Annals of Matematics Annals of Mathematics and Artificial Intelligence Annals of Pure and Applied Logic Annals of the Institute of Statistical Mathematics Applicable Algebra in Engineering, Communication and Computing

38. List Of Publications Of Andrei Morozov (always Out Of Date!) 1. On A countably categorical decidable model without nontrivial recursive automorphisms . Once more on Higman s question, algebra and logic, Vol. http://www.math.nsc.ru/~asm256/Papers.html

List of publications of Andrei Morozov (always out of date!) 1. On decidability of some theories of Boolean algebras with distinguished ideals, in: 5th all-union conference on mathematical logic (abstracts), Novosibirsk 1979, p. 99, in Russian. 2. Countable homogeneous Boolean algebras. In: 14 All-Union algebraic conference. Leningrad, 1981, P. 201-201. in Russian. 3. Recursive automorphism groups of constructive Boolean algebras. In: 6 All-Union conference on Mathematical Logic. Tbilisi, 1982, P. 119-119. In Russian. 4. On decidability of theories of Boolean algebras with distinguished ideal. Siberian Math. Journal, V. 23, No. 1, 1982, P. 199-201. in Russian. 5. Strong constructivizability of countable saturated Boolean algebras. Algebra and Logic, V. 21, No. 2, 1982, P. 130-137. 6. Countable homogeneous Boolean algebras. Algebra and Logic, V. 21, No. 3, 1982, P. 181-190. 7. Constructive Boolean algebras and their automorphisms, PhD thesis, 1982, 104 pages, in Russian. 8. Groups of recursive automorphisms of constructive Boolean algebras. Algebra and Logic, V. 22, No. 2, 1983, P.95-112.

39. Transactions Of The American Mathematical Society algebra Universalis, 19273303, 1984. MR 87g08022. 15. E. Palyutin. The descriptionof categorical quasivarieties. algebra and logic, 1486-111, 1975. http://www.ams.org/tran/1998-350-01/S0002-9947-98-01594-3/home.html

Journals Home Search Author Info Subscribe ... Help ISSN 1088-6850(e) ISSN 0002-9947(p) Previous issue Table of contents Next issue Articles in press ... All issues Minimal sets and varieties Author(s): Keith A. Kearnes; Emil W. Kiss; Matthew A. Valeriote Journal: Trans. Amer. Math. Soc. MSC (1991): Primary 08A05; Secondary 08A40, 08B15 Retrieve article in: PDF DVI TeX PostScript This article is available free of charge Abstract References Similar articles Additional information Abstract: The aim of this paper is twofold. First some machinery is established to reveal the structure of abelian congruences. Then we describe all minimal, locally finite, locally solvable varieties. For locally solvable varieties, this solves problems 9 and 10 of Hobby and McKenzie. We generalize part of this result by proving that all locally finite varieties generated by nilpotent algebras that have a trivial locally strongly solvable subvariety are congruence permutable. References: J. Berman and S. Seif. An approach to tame congruence theory via subtraces.

40. The Leo Apostel Center Invites Everyone To The 47st Of Its Grammar, algebra and logic ************************** Prof. Lambek stillpublishes regularly on categorical logic, still producing highly valued papers, http://pespmc1.vub.ac.be/CLEA/Seminars/Lambek.txt

The Leo Apostel Center invites everyone to the 47st of its interdisciplinary seminars in the Foundations series. In this series CLEA invites scholars that are actively engaged in the research on the foundations of a particular discipline. Their lectures will always be directed to an interdisciplinary audience, and the discussions aim at confronting the foundations of the different disciplines. Grammar, Algebra and Logic ************************** Prof. Em. Jim Lambek, McGill, Montreal ************************************** Monday, April 10, 17.00h, 10F734. About the lecture and speaker: Prof. Lambek is author of some monographs in mathematics, eg. "Completions of categories" (1966), "Torsion theories, additive semantics, and rings of quotients" (1970), but in particular a standard mathematical reference work "Lectures on Rings and Modules" (1966) of which there was a third edition in 1986. He obtained all his degrees at McGill, Montreal. In 1958, he published his first paper on the syntactic calculus, and for a while the "Lambek Grammars" were an essential opponent to "Chomskian Grammars", essentially supported in Europe - contrary to the North Americans who made Chomski win the day. Prof. Lambek then turned his thoughts for most of a decade to ring theory, particularly to rings of quotients, including the above mentioned monographs. Around 1965 he got interested in categories, resulting in a monograph with Phil Scott "Introduction to Higher order Categorical Logic". That same time he renewed his interest in mathematical linguistics, studying formally verb conjugations in French and Latin. Also to be mentioned is a paper "How to program the abacus" in which he invents independently and simultaneously with Marvin Minsky the Minsky machine, which is Turing complete, but conceptually much simpler than the Turing machine. Currently Prof. Lambek still publishes regularly on categorical logic, still producing highly valued papers, and on linguistics, returning to the grammars of syntactic types. In this lecture he will outline his ideas on the latter. (An appreciation of Prof. Lambek by Prof. Barr on the occasion of Jim Lambek's 75th birthday can be found on http://euclid.math.mcgill.ca/triples/lambek/Lambek.biography.html. )

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