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  1. Categorical Topology
  2. Categorical Closure Operators by Gabriele Castellini, 2003-05-15
  3. Categorical Logic and Type Theory (Studies in Logic and the Foundations of Mathematics) (Studies in Logic and the Foundations of Mathematics) by B. Jacobs, 2001-07-01
  4. Goguen Categories: A Categorical Approach to L-fuzzy Relations (Trends in Logic) by Michael Winter, 2007-07-23
  5. Categorical Structure of Closure Operators: With Applications to Topology, Algebra and Discrete Mathematics (Mathematics and Its Applications) by D. Dikranjan, W. Tholen, 1995-10-31
  6. Categorical Perspectives (Trends in Mathematics)
  7. Realizability, Volume 152: An Introduction to its Categorical Side (Studies in Logic and the Foundations of Mathematics) by Jaap van Oosten, 2008-04-16

41. Infinite Trees And Completely Iterative Theories
categorical algebra, La Jolla, 1965, Springer, Berlin, 1966, 84 The Foundations of categorical Model Theory have the same equational logic, preprint, available

42. Bilgi Mathematics Faculty: Prof. Oleg Belegradek
4, 37. On almost categorical theories, Sibirsk. Finitely approximable associative algebra with unsolvable word problem, algebra and Logika 39, no. logic 65, no
Prof. Oleg Belegradek
Ana sayfa / Home
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Tüm dersler / All Courses

ecture Notes
Set Theory:
dvi pdf ps
Algebra: dvi pdf ps
Analysis: dvi pdf ps
Takvim / Calendar 2003-2004
Poizat's Model Theory Book in Russian

CURRICULUM VITAE for Oleg Belegradek Date of birth November 24, 1949 Place of birth Chelyabinsk, Russia Telephone +90 (212) 2162222/198 (office) +90 (212) 2168477 (fax) e-mail address: Degrees Doctor of Science (Mathematics), 1995, Institute of Mathematics, Siberian Branch of the Russian Academy of Science, Novosibirsk Candidate of Science (Mathematics), 1975, Novosibirsk State University Master (Mathematics), 1972, Novosibirsk State University Research areas Algebra, mathematical logic and applications Academic career Kemerovo State University, Department of Mathematics, Section of Algebra and Geometry, 1975-1977: Assistant professor, 1977-1986: Chairman, 1987-1995: Docent, 1995-1999: Professor Istanbul Bilgi University, Department of Mathematics

43. The Leo Apostel Center Invites Everyone To The 47st Of Its
Grammar, algebra and logic ***** Prof. Em. resulting in a monograph with Phil Scott Introduction to Higher order categorical logic .
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 )

44. Diskin's Papers On Mathematics
graphical schemas for conceptual modeling Sketchbased logic vs. transformations and algebraic theories An application of categorical algebra to database
Papers on Mathematics around Databases
This directory contains a collection of papers that could be encompassed by a common title "Towards Algebraic Graph-Based Model Theory for Computer Science" written in a semi-formal manner to display ideas and problems rather than to dictate solutions. The contents is presented in the picture below. The adjoint directory contains papers on applications of the proposed machinery (and can be considered as a kind of justification for the second part of the title). Algebraic Graph-based Model theory for Computer Science via the Efforts of Diskin and Coauthors Model Data Theory Bases ijcis mnfst Algebraic Methodology Artificial Logic Intelligence dmicacp algin Cathegorical Concurrency Programming Model Theory Languages References:
    In preparation.
    S. Ageshin, B. Cadish, I. Beylin, and Z. Diskin. Data modeling in categorical and computational perspectives. Unpublished note aimed at suggesting an overview on mathematics to be employed in DB and PL, 1995. ( Gzipped PostScript , 3 pages, 31617 bytes)
    B. Cadish and Z. Diskin.

45. WoYaa Search Engine - Africa References Online - SCIENCES AND NATURE/MATHEMATICS
This site contains online books and research papers on the subjects of categorical algebra, categorical logic, categorical geometry, lattice theory, universal
Welcome to WoYaa! Your premier African search engine and Web sites directory since 1997. African Web Sites By Country Algeria Angola Benin Botswana Burkina Faso Burundi Cameroon Cape Verde CAR Chad Comoros Congo Djibouti Egypt EQ. Guinea Eritrea Ethiopia Gabon Gambia Ghana Guinea Guinea Bissau Kenya Lesotho Liberia Libya Madagascar Malawi Mali Mauritania Mauritius Morocco Mozambique Namibia Niger Nigeria RD Congo Rwanda Sao Tome Senegal Seychelles Siserra Leone Somalia South Africa Sudan Swaziland Tanzania Togo Tunisia Uganda W. Sahara Zambia Zimbabwe Forums POLITICS


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46. Bibliography Of G.Rosolini
logic, 55, 1990. and Comput., 79, 1988. Rosolini, G. Representation theorems for special pcategories, In categorical algebra and its Applications, Ed.
Power, A. J., Rosolini, G.
Fixpoint operators for domain equations Theoret. Comput. Sci.
Carboni, A., Rosolini, G., Walters, R.F., editors
Theory Appl. Categ.
Robinson, E.P., Rosolini, G.
An abstract look at realizability , In Computer Science Logic '01 , Ed. L. Fribourg , Lectures Notes in Computer Science,
Fiore, M., Rosolini, G.
Domains in H Theoret. Comput. Sci.
Carboni, A., Rosolini, G.
Locally cartesian closed exact completions J.Pure Appl. Alg.
Rosolini, G.
Equilogical spaces and filter spaces Rend. Circ. Mat. Palermo
Rosolini, G.
A note on Cauchy completeness for preorders Riv. Mat. Univ. Parma
Rosolini, G.
Birkdedal, L., van Oosten, J., Rosolini, G., Scott, D. S., editors
Workshop on Realizability Semantics and Applications , Elsevier Science, Electr. Notes in Theo. Comp. Sci., 1999
Rosolini, G., Streicher, Th.
Comparing models of higher type computation , In Workshop on Realizability Semantics and Applications , Ed. Birkdedal, L., van Oosten, J., Rosolini, G., Scott, D. S., Elsevier Science, Electr. Notes in Theo. Comp. Sci., 1999
Birkedal, L., Carboni, A., Rosolini, G., Scott, D. S.

47. Algebra Of Logic Programming
algebra of logic Programming A declarative programming language has two kinds of semantics. The more abstract helps in reasoning about specifications and correctness, while an operational

48. HTML Generated By Txt2html Via TOM
or logic. Text Barr, M. Wells, C. Categories for Computing Science. New a. Further References Borceux, F. Handbook of categorical algebra (Encyclopedia of
Category Theory 80-415/715 Spring 1999 Course Information Place: DH 2122
Time: TR 2:30-3:50 Instructor
Prof. Steve Awodey
Office: Baker 152 (mail Baker 135)
Office Hour: Monday 2-4 or by appointment
Phone: 268-8947
Email: awodey@andrew Overview
Category theory, a branch of abstract algebra, has found many applications in mathematics, logic, and computer science. Like such fields as elementary logic and set theory, category theory provides a basic conceptual apparatus and a collection of formal methods useful for addressing certain kinds of commonly occurring formal and informal problems, particularly those involving structural and functional considerations. This course is intended to acquaint students with these methods, and also to encourage them to reflect on the interrelations between category theory and the other basic formal disciplines. To be followed by a Spring seminar on more advanced topics. Prerequisites
Some familiarity with abstract algebra or logic. Text
Further References
  • Borceux, F.: Handbook of Categorical Algebra (Encyclopedia of Mathematics and its Applications). Cambridge University Press, 1994. Mac Lane, S.: Categories for the Working Mathematician. Springer, 1971. (the standard reference)

Handbook of categorical algebra 3Categories of Sheaves. Locales, Sheaves, Grothendieck Toposes, The Classifying Topos,Elementary Toposes, Internal logic of a
Research topics include mathematical models and theories in the empirical sciences, models and theories in mathematics, category theory, and the use of mathematical structures in theoretical computer science.
Research Bibliography
Mathematical Theories and Models
Scientific Theories and Models
Category Theory
Theoretical Computer Science ... WWW Research Sites
Mathematical Theories and Models
  • Agazzi and Darvas. Philosophy of Mathematics Today. Kluwer Academic Publishers, 1997
  • Anglin and Lambek. The Heritage of Thales. Springer-Verlag, 1995
  • Akin, Ethan. The General Topology of Dynamical Systems. American Mathematical Society, 1993
  • Barwise, Jon. (ed) Handbook of Mathematical Logic. North-Holland,1977
  • Barwise, Jon. "Axioms for Abstract Model Theory" ,Annals of Mathematical Logic 7(1974) 221-265.
  • Bell, John and Machover,Moshe. A Course in Mathematical Logic. North-Holland, 1977
  • Bridge, Jane. Beginning Model Theory. Clarendon Press, 1977
  • Burgess, John and Rosen, Gifeon. A Subject with No Object Oxford Press, 1997

50. From (Alfred Einstead) Newsgroups Sci.logic
Negatives; Intuitionistic vs. Classical logic (4) A categorical algebra For logic (5) Sequents (6) Basic Properties The Cut Rule
From: (Alfred Einstead) Newsgroups: sci.logic Subject: A Simple Formal, Mathematical Definition Of Logic (was: Maths) References: NNTP-Posting-Host: Message-ID: ; L = f; R = g Disjunction: h = [hS,hT]; [f,g]S = f; [f,g]T = g Implication: @ L,R> = f; > = g Failure: f[] = [] Universal: h = ; Ax = h Existential: h = [x:Ex h]; [x:h]Ex = h In addition, new identities may be formed by Substitution: f(T) = g(T) where f(x) = g(x) Here, as far as substitution is concerned, a variable y in the term [y:f], are bound and so the substitution are defined the same way as they were for the quantifier terms Ay.P and Ey.P. Technically, to make this more precise you have to index all the basic items by the propositions involved. So the actual identities would read: f I(B) = f = I(A) f, where f: A -> B h =

51. Rules Of Logic Relational Rules Identity A - A Associativity
Rules Of logic Relational Rules Identity A A Associativity A (x not free in A) categorical algebra Categories I
= f; R = g = h Sums: [f,g] S = f; [f,g] T = g h = [hS,hT] Exponents: f = @ L, R> g = > Failure: I = [] (for type 0) f [] = [] Universals: At = f(t) = h Existentials: [x: f(x)] Et = f(t) [x: h Ex] = h Success: f = *x (y) = f((x,y)) At (x:q_x) = q_t (x) = (y:f(x)) [x:q_x](Et(z)) = q_t(z) where #f = @ <*f , I> %f = * <*f (x)))

52. Chronological List Of Publications
Symbolic logic, Abstract, Vol. 31 (1966), 294295. 5. The Category of Categories as a Foundation for Mathematics, La Jolla Conference on categorical algebra,
F. William Lawvere
Chronological list of publications
HOME Subject Classification Bottom of page (most recent) 1. Functorial Semantics of Algebraic Theories Proceedings of the National Academy of Science 50 , No. 5 (November 1963), 869-872. 2. Elementary Theory of the Category of Sets Proceedings of the National Academy of Science 52 , No. 6 (December 1964), 1506-1511. Algebraic Theories, Algebraic Categories, and Algebraic Functors, Theory of Models ; North-Holland, Amsterdam (1965), 413-418. Functorial Semantics of Elementary Theories Journal of Symbolic Logic , Abstract, Vol. 31 (1966), 294-295. The Category of Categories as a Foundation for Mathematics La Jolla Conference on Categorical Algebra , Springer-Verlag (1966), 1-20. Some Algebraic Problems in the Context of Functorial Semantics of Algebraic Theories Springer Lecture Notes in Mathematics No. 61 , Springer-Verlag (1968), 41-61. Ordinal Sums and Equational Doctrines Springer Lecture Notes in Mathematics No. 80 , Springer-Verlag (1969), 141-155. Diagonal Arguments and Cartesian Closed Categories Springer Lecture Notes in Mathematics No. 92

53. Hidden Algebra
Algebraic Structures, Volume 1 Algebraic Techniques, edited exposition of some basic categorical concepts Stretching First order Equational logic Proofs with
Hidden Algebra Homepage Contents 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.

54. Heyting Algebra - Wikipedia, The Free Encyclopedia
propositional logic formulae, ordered via logical entailment for order which is the desired Heyting algebra. F. Borceux,Handbook of categorical algebra 3, In
Heyting algebra
From Wikipedia, the free encyclopedia.
In mathematics Heyting algebras are special partially ordered sets that constitute a generalization of Boolean algebras . Heyting algebras arise as models of intuitionistic logic , a logic in which the law of excluded middle does not in general hold. Complete Heyting algebras are a central object of study in pointless topology Table of contents 1 Formal definitions 2 Properties 3 Examples 4 References ... edit
Formal definitions
A Heyting algebra H is a bounded lattice such that for all a and b in H there is a greatest element x of H such that a x b . This element is called the relative pseudo-complement of a with respect to b , and is denoted a b (or a b An equivalent definition can be given by considering the mappings f a H H defined by f a x a x , for some fixed a in H . A bounded lattice H is a Heyting algebra iff all mappings f a are the lower adjoint of a monotone Galois connection . In this case the respective upper adjoints g a are given by g a x a x A complete Heyting algebra is a Heyting algebra that is a complete lattice In any Heyting algebra, one can define the

55. Science And Math -The Importance Of Algebra
and Geometry will help train your mind on the logics involved in any contains online books and research papers on categorical geometry and categorical algebra.
Please show your support for this site and visit the sponsors Science And Math - Algebra As much as your math teachers would like you to believe, Algebra will have absolutely nothing to do with the day to day world of the average person... BUT do YOU want to be just average? Advance maths will give you the edge to enter into college programs and help you towards a degree that can mean the difference of $10,000 - $100,000 per year from the average jobs. While you may or may not use Algebra on the job, it will get you through the college years and it is the degree that will help you get far. If you want to get a handle on matters of logic, Algebra and Geometry will help train your mind on the logics involved in any given situation. Knowledge in these subjects, when practiced regularly, can steer you clear of scams, cons, and falling into the wrong circumstances. Those examples were just for the average person on the reason why one should consider studying these subjects with a degree of seriousness. For those who want to use math in their careers, there are many professions that incorporate the skills of Algebra such as the medical profession, science and research, engineering, and anyone who needs to figure out the unknown elements. Algebra is helpful in trying to come up with the solution to a missing element with other given factors (Geometry is the same in this aspect.) Commonly known, you are usually trying to figure out the unknown which is symbolized by a letter of the alphabet. In the equation, you are given a handful of numbers to work with to come up with the answer to the missing element which is represented by the letter. Your job is to figure out the best approach using one of several basic procedures to solve the problem.

56. Publications In Logic
minimal theories II, J. Symbolic logic 37(1972 6. On universal Horn theories categorical in some infinitepower, (with AH Lachlan), algebra Universalis (fasc
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.
  • 57. Logic And Language Links - Categorical Logic
    categorical logic This concept has currently no gloss. categorical logic is a subtopic of algebraic logic. categorical logic has currently no subtopics.
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    under algebraic logic TOP You have selected the concept categorical logic This concept has currently no gloss. categorical logic is a:
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    58. Logic And Language Links - Algebraic Logic
    TOP You have selected the concept algebraic logic This concept has currently no gloss. algebraic logic is a subtopic of algebra 1 subtopic of logical syntax.
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    under algebra 1 TOP You have selected the concept algebraic logic This concept has currently no gloss. algebraic logic is a:
    subtopic of algebra 1
    subtopic of logical syntax
    algebraic logic has the following subtopics:

    59. The Math Forum - Math Library - Algebraic Topology
    Prized Geometric logic Ivars Peterson (MathTrek) Computer programs can handle articles that significantly advance the study of categorical algebra or methods
    Browse and Search the Library
    Math Topics Topology : Algebraic Topology

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    Selected Sites (see also All Sites in this category
  • Algebraic Topology - Dave Rusin; The Mathematical Atlas
    A short article designed to provide an introduction to algebraic topology, the study of algebraic objects attached to topological spaces. The algebraic invariants reflect some of the topological structure of the spaces. The use of these algebraic tools calls attention to some types of topological spaces which are well modeled by the algebra; fibre bundles and related spaces are included here... the use of the algebraic tools also calls attention to the aspects of a topological space which are well modeled by the algebra; this gives rise to homotopy theory. The algebraic tools used in topology include various (co)homology theories, homotopy groups, and groups of maps. These in turn have necessitated the development of more complex algebraic tools such as derived functors and spectral sequences. History, applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus. more>>
  • AT Algebraic Topology (Front for the Mathematics ArXiv) - Univ. of California, Davis
  • 60. Information And Computation -- 1995
    Algebraic theories for namepassing calculi. GL McColm. Pebble games and subroutines in least fixed point logic. A categorical linear framework for Petri nets.
    Information and Computation 1995
    Volume 116, Number 1, January 1995

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