A Functorial Model Theory
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A Functorial Model Theory
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Author : Cyrus F. Nourani
language : en
Publisher: CRC Press
Release Date : 2016-04-19
A Functorial Model Theory written by Cyrus F. Nourani and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Mathematics categories.
This book is an introduction to a functorial model theory based on infinitary language categories. The author introduces the properties and foundation of these categories before developing a model theory for functors starting with a countable fragment of an infinitary language. He also presents a new technique for generating generic models with categories by inventing infinite language categories and functorial model theory. In addition, the book covers string models, limit models, and functorial models.
Functor Categories Model Theory Algebraic Analysis And Constructive Methods
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Author : Alexander Martsinkovsky
language : en
Publisher: Springer Nature
Release Date : 2024-05-04
Functor Categories Model Theory Algebraic Analysis And Constructive Methods written by Alexander Martsinkovsky and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-04 with Mathematics categories.
This volume comprises selected contributions by the participants of the second "Functor Categories, Model Theory, Algebraic Analysis and Constructive Methods" conference, which took place at the University of Almería, Spain, in July 2022. The conference was devoted to several seemingly unrelated fields: functor categories, model theory of modules, algebraic analysis (including linear control systems), and constructive category theory, to mention just a few. The fact that these fields are actually related is a very recent realization. The connections between these disciplines are changing in real time, and the goal of this volume is to provide an initial reference point for this emerging interdisciplinary field. Besides research articles, the volume includes two extended lectures: one on constructive methods in algebraic analysis and the other on the functorial approach to algebraic systems theory. Hence, in addition to its interestfor researchers, the volume will also be an invaluable resource for newcomers.
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.
Institution Independent Model Theory
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Author : Răzvan Diaconescu
language : en
Publisher: Springer Nature
Release Date : 2025-03-05
Institution Independent Model Theory written by Răzvan Diaconescu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-05 with Mathematics categories.
A model theory that is independent of any concrete logical system allows a general handling of a large variety of logics. This generality can be achieved by applying the theory of institutions that provides a precise general mathematical formulation for the intuitive concept of a logical system. Especially in computer science, where the development of a huge number of specification logics is observable, institution-independent model theory simplifies and sometimes even enables a concise model-theoretic analysis of the system. Besides incorporating important methods and concepts from conventional model theory, the proposed axiomatic top-down methodology allows for a structurally clean understanding of model-theoretic phenomena. Consequently, results from conventional concrete model theory can be understood more easily, and sometimes even new results are obtained. Moreover, all this is also applied to non-classical model theories. This second edition introduces some novelties in the presentation style which aim to enhance the readability of the material and the proofs. Additional chapters have also been added.
Model Theory And Topoi
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Author : F.W. Lawvere
language : en
Publisher: Springer
Release Date : 2006-11-15
Model Theory And Topoi written by F.W. Lawvere 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.
A Collection of Lectures by Variuos Authors
Algebraic Computability And Enumeration Models
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Author : Cyrus F. Nourani
language : en
Publisher: CRC Press
Release Date : 2016-02-24
Algebraic Computability And Enumeration Models written by Cyrus F. Nourani and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-24 with Mathematics categories.
This book, Algebraic Computability and Enumeration Models: Recursion Theory and Descriptive Complexity, presents new techniques with functorial models to address important areas on pure mathematics and computability theory from the algebraic viewpoint. The reader is first introduced to categories and functorial models, with Kleene algebra examples
Recursive Model Theory
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Author :
language : en
Publisher: Elsevier
Release Date : 1998-11-30
Recursive Model Theory written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-11-30 with Computers categories.
Recursive Model Theory
The Theory Of Models
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Author : J.W. Addison
language : en
Publisher: Elsevier
Release Date : 2014-05-27
The Theory Of Models written by J.W. Addison and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-27 with Mathematics categories.
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.
Axiomatic Method And Category Theory
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Author : Andrei Rodin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-10-14
Axiomatic Method And Category Theory written by Andrei Rodin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-14 with Philosophy categories.
This volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia. The author, a well-known philosopher and historian of mathematics, first examines Euclid, who is considered the father of the axiomatic method, before moving onto Hilbert and Lawvere. He then presents a deep textual analysis of each writer and describes how their ideas are different and even how their ideas progressed over time. Next, the book explores category theory and details how it has revolutionized the notion of the axiomatic method. It considers the question of identity/equality in mathematics as well as examines the received theories of mathematical structuralism. In the end, Rodin presents a hypothetical New Axiomatic Method, which establishes closer relationships between mathematics and physics. Lawvere's axiomatization of topos theory and Voevodsky's axiomatization of higher homotopy theory exemplify a new way of axiomatic theory building, which goes beyond the classical Hilbert-style Axiomatic Method. The new notion of Axiomatic Method that emerges in categorical logic opens new possibilities for using this method in physics and other natural sciences. This volume offers readers a coherent look at the past, present and anticipated future of the Axiomatic Method.
Institution Independent Model Theory
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Author : Razvan Diaconescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-08-01
Institution Independent Model Theory written by Razvan Diaconescu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-01 with Mathematics categories.
This book develops model theory independently of any concrete logical system or structure, within the abstract category-theoretic framework of the so called ‘institution theory’. The development includes most of the important methods and concepts of conventional concrete model theory at the abstract institution-independent level. Consequently it is easily applicable to a rather large diverse collection of logics from the mathematical and computer science practice.