First Order Categorical Logic
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First Order Categorical Logic
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Author : M. Makkai
language : en
Publisher: Springer
Release Date : 2006-11-15
First Order Categorical Logic written by M. Makkai and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
First Order Categorical Logic
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Author : M. Makkai
language : en
Publisher:
Release Date : 2014-09-01
First Order Categorical Logic written by M. Makkai and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.
Lecture Notes In Mathematics
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Author :
language : en
Publisher:
Release Date : 1964
Lecture Notes In Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964 with Categories (Mathematics) categories.
Introduction To Higher Order Categorical Logic
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Author : J. Lambek
language : en
Publisher: Cambridge University Press
Release Date : 1988-03-25
Introduction To Higher Order Categorical Logic written by J. Lambek and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-03-25 with Mathematics categories.
Part I indicates that typed-calculi are a formulation of higher-order logic, and cartesian closed categories are essentially the same. Part II demonstrates that another formulation of higher-order logic is closely related to topos theory.
Introduction To Higher Order Categorical Logic
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Author : Joachim Lambek
language : en
Publisher:
Release Date : 1988
Introduction To Higher Order Categorical Logic written by Joachim Lambek and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Categories (Mathematics) categories.
Categorical Logic And Type Theory
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Author : B. Jacobs
language : en
Publisher: Gulf Professional Publishing
Release Date : 2001-05-10
Categorical Logic And Type Theory written by B. Jacobs and has been published by Gulf Professional Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-05-10 with Computers categories.
This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.
Accessible Categories The Foundations Of Categorical Model Theory
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Author : Mihály Makkai
language : en
Publisher: American Mathematical Soc.
Release Date : 1989
Accessible Categories The Foundations Of Categorical Model Theory written by Mihály Makkai and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
Intended for category theorists and logicians familiar with basic category theory, this book focuses on categorical model theory, which is concerned with the categories of models of infinitary first order theories, called accessible categories. The starting point is a characterization of accessible categories in terms of concepts familiar from Gabriel-Ulmer's theory of locally presentable categories. Most of the work centers on various constructions (such as weighted bilimits and lax colimits), which, when performed on accessible categories, yield new accessible categories. These constructions are necessarily 2-categorical in nature; the authors cover some aspects of 2-category theory, in addition to some basic model theory, and some set theory. One of the main tools used in this study is the theory of mixed sketches, which the authors specialize to give concrete results about model theory. Many examples illustrate the extent of applicability of these concepts. In particular, some applications to topos theory are given. Perhaps the book's most significant contribution is the way it sets model theory in categorical terms, opening the door for further work along these lines. Requiring a basic background in category theory, this book will provide readers with an understanding of model theory in categorical terms, familiarity with 2-categorical methods, and a useful tool for studying toposes and other categories.
Topoi
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Author : R. Goldblatt
language : en
Publisher: Elsevier
Release Date : 2014-06-28
Topoi written by R. Goldblatt and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-28 with Mathematics categories.
The first of its kind, this book presents a widely accessible exposition of topos theory, aimed at the philosopher-logician as well as the mathematician. It is suitable for individual study or use in class at the graduate level (it includes 500 exercises). It begins with a fully motivated introduction to category theory itself, moving always from the particular example to the abstract concept. It then introduces the notion of elementary topos, with a wide range of examples and goes on to develop its theory in depth, and to elicit in detail its relationship to Kripke's intuitionistic semantics, models of classical set theory and the conceptual framework of sheaf theory (``localization'' of truth). Of particular interest is a Dedekind-cuts style construction of number systems in topoi, leading to a model of the intuitionistic continuum in which a ``Dedekind-real'' becomes represented as a ``continuously-variable classical real number''.The second edition contains a new chapter, entitled Logical Geometry, which introduces the reader to the theory of geometric morphisms of Grothendieck topoi, and its model-theoretic rendering by Makkai and Reyes. The aim of this chapter is to explain why Deligne's theorem about the existence of points of coherent topoi is equivalent to the classical Completeness theorem for ``geometric'' first-order formulae.
Uncountably Categorical Theories
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Author : Boris Zilber
language : en
Publisher: American Mathematical Soc.
Release Date :
Uncountably Categorical Theories written by Boris Zilber and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
The 1970s saw the appearance and development in categoricity theory of a tendency to focus on the study and description of uncountably categorical theories in various special classes defined by natural algebraic or syntactic conditions. There have thus been studies of uncountably categorical theories of groups and rings, theories of a one-place function, universal theories of semigroups, quasivarieties categorical in infinite powers, and Horn theories. In Uncountably Categorical Theories , this research area is referred to as the special classification theory of categoricity. Zilber's goal is to develop a structural theory of categoricity, using methods and results of the special classification theory, and to construct on this basis a foundation for a general classification theory of categoricity, that is, a theory aimed at describing large classes of uncountably categorical structures not restricted by any syntactic or algebraic conditions.
Mathematical Logic And Formalized Theories
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Author : Robert L. Rogers
language : en
Publisher: Elsevier
Release Date : 2014-05-12
Mathematical Logic And Formalized Theories written by Robert L. Rogers and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-12 with Mathematics categories.
Mathematical Logic and Formalized Theories: A Survey of Basic Concepts and Results focuses on basic concepts and results of mathematical logic and the study of formalized theories. The manuscript first elaborates on sentential logic and first-order predicate logic. Discussions focus on first-order predicate logic with identity and operation symbols, first-order predicate logic with identity, completeness theorems, elementary theories, deduction theorem, interpretations, truth, and validity, sentential connectives, and tautologies. The text then tackles second-order predicate logic, as well as second-order theories, theory of definition, and second-order predicate logic F2. The publication takes a look at natural and real numbers, incompleteness, and the axiomatic set theory. Topics include paradoxes, recursive functions and relations, Gödel's first incompleteness theorem, axiom of choice, metamathematics of R and elementary algebra, and metamathematics of N. The book is a valuable reference for mathematicians and researchers interested in mathematical logic and formalized theories.