Proceedings Of The American Mathematical Society School of algebra and logic, Consultants Bureau, New York, 2000. MR 2002a03069. 5. Goncharov, Sergei S., Constructive models of categorical theories, Mat. http://www.ams.org/proc/2003-131-12/S0002-9939-03-06951-X/home.html
Extractions: Retrieve article in: PDF DVI TeX PostScript ... Additional information Abstract: We prove that if is any model of a trivial, strongly minimal theory, then the elementary diagram is a model complete -theory. We conclude that all countable models of a trivial, strongly minimal theory with at least one computable model are -decidable, and that the spectrum of computable models of any trivial, strongly minimal theory is References: Baldwin, John T. and Lachlan, Alistair H.
Foundations, Combinatorics & Logic - Cambridge University Press Cambridge books covering mathematical logic, category theory, set theory and mathematical For the first time in a textbook, categorical algebra is used to http://publishing.cambridge.org/stm/mathematics/foundations/
Unisa Online - Pure Mathematics JFT Hartney. categorical algebra and Topology, Prof. IW Alderton. M. Frick. Functional Analysis and Operator algebras. Prof. L. Labuschagne. Mathematical logic, Prof. http://www.unisa.ac.za/default.asp?Cmd=ViewContent&ContentID=1673
Project Euclid Journals S., ``Constructive models of $ømega_1$categorical theories, Matematicheskie Strong constructivability of homogeneous models, algebra and logic, vol. http://projecteuclid.org/Dienst/UI/1.0/Display/euclid.ndjfl/1039724885
Extractions: Current Issue Past Issues Search this Journal Editorial Board ... Note on Volumes 35-40 Bakhadyr Khoussainov Andre Nies , and Richard A. Shore Source: Notre Dame J. Formal Logic Abstract: In this paper we investigate computable models of -categorical theories and Ehrenfeucht theories. For instance, we give an example of an -categorical but not -categorical theory such that all the countable models of except its prime model have computable presentations. We also show that there exists an -categorical but not -categorical theory such that all the countable models of except the saturated model, have computable presentations. References Primary Subjects:
Science, Math, Logic And Foundations: People E. University of Cambridge - categorical logic, game semantics Rolla - Pure and Applied logic, Foundations, Harmonic Analysis, algebra, Metric Spaces http://www.combose.com/Science/Math/Logic_and_Foundations/People/
Extractions: Aczel, Peter - University of Manchester - Philosophy and Foundations of Mathematics and Computing, Mathematical Logic, Categorical Logic. Andrews, Peter B. - Carnegie Mellon University - type theory, automated theorem proving. Avigad, Jeremy - Carnegie Mellon University - proof theory, constructive mathematics, proof complexity, and the history and philosophy of mathematics. Awodey, Steve - Carnegie Mellon University - Category theory, logic, history and philosophy of mathematics and logic. Baldwin, John T. - University of Illinois, Chicago - Model theory (finite and infinite). Barendregt, Henk - University of Nijmegen - Lambda calculus, type theory and formalising mathematical vernacular. Bartoszynski, Tomek - Boise State University - Set theory. Bellin, Gianluigi - University of Leeds - Proof theory, the formulae-as-types correspondence and semantics of programming languages. Berline, Chantal - University of Paris 7 - Lambda calculus. Blass, Andreas R. - University of Michigan, Ann Arbor - Set theory, finite combinatorics, theoretical computer science. Bolotov, Alexander
BIBLIOGRAPHY About DESCENT And CATEGORY THEORY! A. Obtu \book The logic of categories of partial book Introduction to categories, homological algebra, and sheaf Von Eye , et al \book categorical Variables in http://north.ecc.edu/alsani/catbib.html
Extractions: BIBLIOGRAPHY about DESCENT THEORY from W. Tholen home page. Monades et Descente Selected Topics in Algebra An Outline of a Theory of Higher Dimensional Descent The Theory of Descent Triples and Descent An Extension of the Galois Theory of Grothendieck Theory of Categories over a Base Topos Descent Theory for Toposes Effective Descent Morphisms and Effective Equivalence Relations Introduction to Affine Group Schemes BIBLIOGRAPHY about CATEGORY THEORY F. W. Lawvere publications: http://www.acsu.buffalo.edu/~wlawvere Back to Descent and Category Theory WebPage
5 De Morgan's Life And Work Figure 2 De Morgan s notation for the categorical forms AOEI. Besides his work in algebra and logic, De Morgan contributed 712 articles to the ``Penny http://www.hf.uio.no/filosofi/njpl/vol2no1/history/node5.html
Extractions: Next: 6 Boole's Life Up: A Brief History of Previous: 4 British Mathematics in Augustus de Morgan was born as fifth child on the 27th of June 1806 in Madura, India, where his father worked as an officer for the East India Company. His family soon moved to England, where they lived first at Worcester and then at Taunton. His early education was in private schools, where he enjoyed a classic education in Latin, Greek, Hebrew, and mathematics. In 1823, at the age of 16, he entered Trinity College in Cambridge, where the work of the ``Analytical Society'' had already changed the students' schedule so that De Morgan also studied Continental mathematics. In 1826, he graduated as a fourth Wrangler and turned his back on mathematics to study to be a lawyer at Lincoln's Inn in London. But only a year later he revised this decision and applied for a position as professor of mathematics at the newly established University College in London. At the age of 22, with no publications, he was appointed. The work that De Morgan produced in the years to come spanned a wide variety of subjects with an emphasis on algebra and logic. But surprisingly he was not able to connect them. An important work of his was the ``Elements of Arithmetic'', published in 1830, containing a simple yet thorough philosophical treatment of the ideas of number and magnitude. In a paper from 1838 he formally described the concept of mathematical induction and in 1849 in ``Trigonometry and Double Algebra'' he gave a geometrical interpretation of complex numbers.
List Of Publications Of Andrei Morozov Once more on countably categorical theories, Siberian mathematical journal, 1999, Vol. 40, No. 2. 63. Once more on Higman s question, algebra and logic, Vol. http://www.math.nsc.ru/~asm256/Papers.html
International Conference Logic And Applications Trofimov AV, Countably categorical Boolean algebras with distinguished Ershov subalgebras. OV, Representability of functions of the algebra of logic by sums of http://www.math.nsc.ru/conference/malmeet/ershov/abse.html
Extractions: "Logic and Applications" Accepted abstracts Abdykhalykov A. T. Metabelian Leibnitz algebras Abutalipova Sh. U. Inclusion problem for bi-modules over polynomial rings Akhtyamov R. B. On index sets Ashaev I. V. Analogues of the arithmetical hierarchy in generalized computability Badaev S. A., Goncharov S. S. Ershov's problems on minimal numberings Baizhanov B. S. Types and expansions of models of weakly o-minimal and stable theories by unary predicates Bardakov V. G. A property of groups with subexponential growth Bazhanov V. A. The problem of assimilation of great discoveries in the history of logic Belyakin N. V., Ganov V. A. A modification of the choice principle Belyakin N. V., Pobedin L. N. Towards an alternative infinity Bel'tyukov A. P. A complexity hierarchy of finite equi-accessable address machines Biryukov P. A., Mishkin V. V. Set ideals with isomorphic symmetry groups Bludov V. V. Geometrical equivalence of groups and quasivarieties Boiko V. A. Lobachevskii and Kant Bredikhin D. A. N -variables logic and Jonsson's algebra of relations Budkin A. I.
A Reflective Module Algebra With Applications To The Maude Language OBJ embodies many of the categorical module composition ole in the development of algebraic specification, and theorem proving in 2OBJ, and logic programming in http://maude.cs.uiuc.edu/papers/abstract/Dmodalg_1999.html
Extractions: It has long been recognized that large specifications are unmanageable unless they are built in a structured fashion from smaller specifications using specification-building operations. Modularity and module composition are central notions for specification languages and declarative programming languages. Although Parnas is the author of the possibly earliest work on software modules, Burstall and Goguen were the first to study the semantics of modular specifications and their composition operations in their language Clear. They proposed the idea of ``putting theories together'' by composing them through operations having a clean and logic-independent categorical semantics. Continuing in this line of work, Burstall and Goguen captured the minimal requirements that a logic must meet to be a reasonable specification framework and introduced the notion of institution Categorical techniques have allowed since then the study of specification-building operations with independence of any specific formalism by different authors, giving rise to a large body of research. Algebraic specification is now a mature field of Computer Science because of its mathematical foundations. After Clear, the theory of algebraic specification has been implemented in many computing systems, such as OBJ, ACT ONE, ASL, ASF, PLUSS, LPG, Larch, CASL, etc., and has become an important technique in software engineering methodologies.
Stone Duality Between Queries And Data - Benson (ResearchIndex) 1996 1 Richard Hull Victor Vianu (context) Abiteboul - 1995 1 The logic of structures (context) - Ageron - 1992 1 Handbook of categorical algebra 1 Basic http://citeseer.ist.psu.edu/benson96stone.html
Logic And Foundations: People University of Cambridge categorical logic, game semantics and Rolla - Pure and Applied logic, Foundations, Harmonic Analysis, algebra, Metric Spaces http://www.puredirectory.com/Science/Math/Logic-and-Foundations/People/
Extractions: Home Science Math Logic and Foundations : People Students and Independent Scholars google_ad_client = "pub-3272565765518472";google_alternate_color = "FFFFFF";google_ad_width = 336;google_ad_height = 280;google_ad_format = "336x280_as";google_ad_channel ="7485447737";google_color_border = "FFFFFF";google_color_bg = "FFFFFF";google_color_link = "0000FF";google_color_url = "008000";google_color_text = "000000"; Standard Listings
EpistemeLinks.com: Journals Results as they have philosophical interest, those aspects of symbolic logic and of the articles that significantly advance the study of categorical algebra or methods http://www.epistemelinks.com/Main/journals.aspx?Format=Both&TopiCode=Math
Publications - G. Cherlin of small Morley rank, Annals of Mathematical logic 17 (1979), 128. 13. On totally categorical groups (with W. Baur and A. Macintyre), J. algebra 57 (1979), 407 http://www.math.rutgers.edu/~cherlin/Paper/older.html
Extractions: Last first. May include some items submitted or in preparation Recent publications Older publications: 69. Minimal antichains in well-founded quasi-orders with an application to tournaments, with B. Latka J. Combinatorial Theory Series B. 68. Forbidden subgraphs and forbidden substructures, with N. Shi, J. Symbolic Logic Groups of finite Morley rank and even type with strongly closed abelian subgroups, with T. Altinel and A. Borovik J. Algebra 66. The classification of finite homogeneous groups (with U. Felgner) J. London Math. Society 65. Sporadic homogeneous structures 64. Infinite imprimitive homogeneous 3-edge-colored complete graphs, JSL offprints available 63. Central extensions of algebraic groups of finite Morley rank, with T. Altinel, JSL offprints available 62. A Hall theorem for omega -stable groups, with T. Altinel, L.-J. Corredor, and A. Nesin, J. London Math. Society, 13 pp. J. London Math. Soc. offprints available 61. On groups of finite Morley rank with weakly embedded subgroups, with T. Altinel and A. Borovik
Category Theory Resources by F. William Lawvere Applications algebra in a by Benjamin C. Pierce Sets, logic and Categories Hopf Models of Sharing Graphs A categorical Semantics of Let http://futuresedge.org/mathematics/Category_Theory.html
Extractions: Vector spaces, say over the rationals, algebraically closed fields of a given characteristic, and free groups are three examples of classes of mathematical structures which are categorical in all uncountable cardinals, i.e. any two uncountable such structures of the same size are isomorphic. In each of these instances, there is a notion of dimension (linear dimension, transcendence degree, the number of generators) which captures the isomorphism-type of the structure. This is a general model-theoretic phenomenon: Th: (Lessmann) If K is a reasonable class of mathematical structures which is categorical in some uncountable cardinal, then inside each mathematical structure there is a pregeometry whose dimension determines the isomorphism-type of the mathematical structure, and furthermore, the class is categorical in all uncountable cardinals. By reasonable, we mean (1) axiomatised using at most countably many first order axioms (the first two examples above, in this case this is the classical Baldwin-Lachlan theorem), or, more generally, (2) axiomatised using not necessarily first order axioms but in such a way that there is a good notion of universal domain (a homogeneous model as in the example of free groups, or a full model). The difficulty in (2) is that the compactness theorem fails. The use of dimension theory to understand mathematical structures works beyond can categoricity: Inside any mathematical structure, we can define what we mean by "A is independent from B (over C)" using the automorphism group of the structure. This independence relation has good properties under very general model-theoretic circumstances, called simplicity and stability (shown by Buechler-Lessmann). Examples of stable and simple mathematical structures are those described above (in each case the independence relation becomes the familiar one: in vector spaces it becomes linear independence, and alebraic independence in an algebraically closed field), as well as Hilbert spaces, where the independence relation coincides with orthogonality.
Observational Logic, Constructor-based Logic, And Their Duality 11 F, Borceux, Handbook of categorical algebra, Cambridge University Hiding More of Hidden algebra, Proceedings of M. Bidoit, Observational logic (long version http://portal.acm.org/citation.cfm?id=773695&dl=ACM&coll=portal&CFID=11111111&CF
