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Author: Bradd T. Hart Publisher: American Mathematical Soc. ISBN: 9780821872819 Category : Mathematics Languages : en Pages : 426
Book Description
This book deals with the main themes in Mihaly Makkai's research career: traditional model theory, categorical model theory and logics, and higher-dimensional category theory. Included are both research papers and survey papers, giving useful material for experts and students in these fields. Particularly valuable are papers that show how the techniques and understanding in one field can be productively applied to another; examples are the paper by Harnik, which explains how Shelah's $T^{eq}$ construction (in model theory) is the same as the categorical notion of pretopos completion; the paper by Kamensky, which gives category-theoretic treatments of sophisticated notions from stability theory; and the paper by Prest relating categorical logic and the model theory of modules. These and other papers in this volume should make this a valuable resource for any mathematician interested in classical or categorical model theory or higher dimensional category theory.
Author: Bradd T. Hart Publisher: American Mathematical Soc. ISBN: 9780821872819 Category : Mathematics Languages : en Pages : 426
Book Description
This book deals with the main themes in Mihaly Makkai's research career: traditional model theory, categorical model theory and logics, and higher-dimensional category theory. Included are both research papers and survey papers, giving useful material for experts and students in these fields. Particularly valuable are papers that show how the techniques and understanding in one field can be productively applied to another; examples are the paper by Harnik, which explains how Shelah's $T^{eq}$ construction (in model theory) is the same as the categorical notion of pretopos completion; the paper by Kamensky, which gives category-theoretic treatments of sophisticated notions from stability theory; and the paper by Prest relating categorical logic and the model theory of modules. These and other papers in this volume should make this a valuable resource for any mathematician interested in classical or categorical model theory or higher dimensional category theory.
Author: J.W. Addison Publisher: Elsevier ISBN: 1483275345 Category : Mathematics Languages : en Pages : 513
Book Description
Studies in Logic and the Foundations of Mathematics: The Theory of Models covers the proceedings of the International Symposium on the Theory of Models, held at the University of California, Berkeley on June 25 to July 11, 1963. The book focuses on works devoted to the foundations of mathematics, generally known as "the theory of models." The selection first discusses the method of alternating chains, semantic construction of Lewis's systems S4 and S5, and continuous model theory. Concerns include ordered model theory, 2-valued model theory, semantics, sequents, axiomatization, formulas, axiomatic approach to hierarchies, alternating chains, and difference hierarchies. The text also ponders on Boolean notions extended to higher dimensions, elementary theories with models without automorphisms, and applications of the notions of forcing and generic sets. The manuscript takes a look at a hypothesis concerning the extension of finite relations and its verification for certain special cases, theories of functors and models, model-theoretic methods in the study of elementary logic, and extensions of relational structures. The text also reviews relatively categorical and normal theories, algebraic theories, categories, and functors, denumerable models of theories with extra predicates, and non-standard models for fragments of number theory. The selection is highly recommended for mathematicians and researchers interested in the theory of models.
Author: Alberto Facchini Publisher: American Mathematical Soc. ISBN: 1470443678 Category : Mathematics Languages : en Pages : 250
Book Description
This volume contains the proceedings of the international conference Model Theory of Modules, Algebras and Categories, held from July 28–August 2, 2017, at the Ettore Majorana Foundation and Centre for Scientific Culture in Erice, Italy. Papers contained in this volume cover recent developments in model theory, module theory and category theory, and their intersection.
Author: Elaine M. Landry Publisher: Oxford University Press ISBN: 019874899X Category : Mathematics Languages : en Pages : 486
Book Description
This is the first volume on category theory for a broad philosophical readership. It is designed to show the interest and significance of category theory for a range of philosophical interests: mathematics, proof theory, computation, cognition, scientific modelling, physics, ontology, the structure of the world. Each chapter is written by either a category-theorist or a philosopher working in one of the represented areas, in an accessible waythat builds on the concepts that are already familiar to philosophers working in these areas.
Author: Jose Iovino Publisher: CRC Press ISBN: 0429554192 Category : Mathematics Languages : en Pages : 327
Book Description
A coherent introduction to current trends in model theory Contains articles by some of the most influential logicians of the last hundred years. No other publication brings these distinguished authors together Suitable as a reference for advanced undergraduate, postgraduates, and researchers Material presented in the book (e.g, abstract elementary classes, first-order logics with dependent sorts, and applications of infinitary logics in set theory) is not easily accessible in the current literature The various chapters in the book can be studied independently.
Author: John T. Baldwin Publisher: Cambridge University Press ISBN: 110810021X Category : Science Languages : en Pages : 365
Book Description
Major shifts in the field of model theory in the twentieth century have seen the development of new tools, methods, and motivations for mathematicians and philosophers. In this book, John T. Baldwin places the revolution in its historical context from the ancient Greeks to the last century, argues for local rather than global foundations for mathematics, and provides philosophical viewpoints on the importance of modern model theory for both understanding and undertaking mathematical practice. The volume also addresses the impact of model theory on contemporary algebraic geometry, number theory, combinatorics, and differential equations. This comprehensive and detailed book will interest logicians and mathematicians as well as those working on the history and philosophy of mathematics.
Author: Hans Halvorson Publisher: Cambridge University Press ISBN: 1107110998 Category : Philosophy Languages : en Pages : 305
Book Description
Reconsiders the role of formal logic in the analytic approach to philosophy, using cutting-edge mathematical techniques to elucidate twentieth-century debates.
Author: Gilles Dowek Publisher: Springer ISBN: 3319089188 Category : Mathematics Languages : en Pages : 506
Book Description
This book constitutes the refereed proceedings of the Joint 25th International Conference on Rewriting Techniques and Applications, RTA 2014, and 12th International Conference on Typed Lambda-Calculi and Applications, TLCA 2014, held as part of the Vienna Summer of Logic, VSL 2014, in Vienna, Austria, in July 2014. The 28 revised full papers and 3 short papers presented were carefully reviewed and selected from 87 submissions. The papers provide research results on all aspects of rewriting and typed lambda calculi, ranging from theoretical and methodological issues to applications in various contexts. They address a wide variety of topics such as algorithmic aspects, implementation, logic, types, semantics, and programming.
Author: Bradd T. Hart
Author: Bradd T. Hart
Author: Bradd T. Hart
Author: J.W. Addison
Author: Alberto Facchini
Author: Alexander Martsinkovsky
Author: Elaine M. Landry
Author: Jose Iovino
Author: John T. Baldwin
Author: Hans Halvorson
Author: Gilles Dowek