Introduction To Model Theory
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Model Theory An Introduction
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Author : David Marker
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-06
Model Theory An Introduction written by David Marker 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 2006-04-06 with Mathematics categories.
Assumes only a familiarity with algebra at the beginning graduate level; Stresses applications to algebra; Illustrates several of the ways Model Theory can be a useful tool in analyzing classical mathematical structures
Introduction To Model Theory
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Author : Philipp Rothmaler
language : en
Publisher: CRC Press
Release Date : 2018-12-07
Introduction To Model Theory written by Philipp Rothmaler and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-07 with Mathematics categories.
Model theory investigates mathematical structures by means of formal languages. So-called first-order languages have proved particularly useful in this respect. This text introduces the model theory of first-order logic, avoiding syntactical issues not too relevant to model theory. In this spirit, the compactness theorem is proved via the algebraically useful ultrsproduct technique (rather than via the completeness theorem of first-order logic). This leads fairly quickly to algebraic applications, like Malcev's local theorems of group theory and, after a little more preparation, to Hilbert's Nullstellensatz of field theory. Steinitz dimension theory for field extensions is obtained as a special case of a much more general model-theoretic treatment of strongly minimal theories. There is a final chapter on the models of the first-order theory of the integers as an abelian group. Both these topics appear here for the first time in a textbook at the introductory level, and are used to give hints to further reading and to recent developments in the field, such as stability (or classification) theory.
A Course In Model Theory
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Author : Bruno Poizat
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
A Course In Model Theory written by Bruno Poizat 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 2012-12-06 with Mathematics categories.
Translated from the French, this book is an introduction to first-order model theory. Starting from scratch, it quickly reaches the essentials, namely, the back-and-forth method and compactness, which are illustrated with examples taken from algebra. It also introduces logic via the study of the models of arithmetic, and it gives complete but accessible exposition of stability theory.
Mathematical Logic And Model Theory
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Author : Alexander Prestel
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-21
Mathematical Logic And Model Theory written by Alexander Prestel 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 2011-08-21 with Mathematics categories.
Mathematical Logic and Model Theory: A Brief Introduction offers a streamlined yet easy-to-read introduction to mathematical logic and basic model theory. It presents, in a self-contained manner, the essential aspects of model theory needed to understand model theoretic algebra. As a profound application of model theory in algebra, the last part of this book develops a complete proof of Ax and Kochen's work on Artin's conjecture about Diophantine properties of p-adic number fields. The character of model theoretic constructions and results differ quite significantly from that commonly found in algebra, by the treatment of formulae as mathematical objects. It is therefore indispensable to first become familiar with the problems and methods of mathematical logic. Therefore, the text is divided into three parts: an introduction into mathematical logic (Chapter 1), model theory (Chapters 2 and 3), and the model theoretic treatment of several algebraic theories (Chapter 4). This book will be of interest to both advanced undergraduate and graduate students studying model theory and its applications to algebra. It may also be used for self-study.
Introduction To Model Theory
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Author : John Lane Bell
language : en
Publisher:
Release Date : 1965
Introduction To Model Theory written by John Lane Bell and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Model theory categories.
An Invitation To Model Theory
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Author : Jonathan Kirby
language : en
Publisher: Cambridge University Press
Release Date : 2019-04-18
An Invitation To Model Theory written by Jonathan Kirby 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 2019-04-18 with Mathematics categories.
An innovative and largely self-contained textbook bringing model theory to an undergraduate audience.
A Shorter Model Theory
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Author : Wilfrid Hodges
language : en
Publisher: Cambridge University Press
Release Date : 1997-04-10
A Shorter Model Theory written by Wilfrid Hodges 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 1997-04-10 with Mathematics categories.
This is an up-to-date textbook of model theory taking the reader from first definitions to Morley's theorem and the elementary parts of stability theory. Besides standard results such as the compactness and omitting types theorems, it also describes various links with algebra, including the Skolem-Tarski method of quantifier elimination, model completeness, automorphism groups and omega-categoricity, ultraproducts, O-minimality and structures of finite Morley rank. The material on back-and-forth equivalences, interpretations and zero-one laws can serve as an introduction to applications of model theory in computer science. Each chapter finishes with a brief commentary on the literature and suggestions for further reading. This book will benefit graduate students with an interest in model theory.
A Course In Model Theory
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Author : Katrin Tent
language : en
Publisher: Cambridge University Press
Release Date : 2012-03-08
A Course In Model Theory written by Katrin Tent 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 2012-03-08 with Mathematics categories.
Concise introduction to current topics in model theory, including simple and stable theories.
Model Theory And Algebraic Geometry
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Author : Elisabeth Bouscaren
language : en
Publisher: Springer
Release Date : 2009-03-14
Model Theory And Algebraic Geometry written by Elisabeth Bouscaren and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-14 with Mathematics categories.
This introduction to the recent exciting developments in the applications of model theory to algebraic geometry, illustrated by E. Hrushovski's model-theoretic proof of the geometric Mordell-Lang Conjecture starts from very basic background and works up to the detailed exposition of Hrushovski's proof, explaining the necessary tools and results from stability theory on the way. The first chapter is an informal introduction to model theory itself, making the book accessible (with a little effort) to readers with no previous knowledge of model theory. The authors have collaborated closely to achieve a coherent and self- contained presentation, whereby the completeness of exposition of the chapters varies according to the existence of other good references, but comments and examples are always provided to give the reader some intuitive understanding of the subject.
Introduction To Mathematical Logic
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Author : Jerome Malitz
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Mathematical Logic written by Jerome Malitz 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 2012-12-06 with Mathematics categories.
This book is intended as an undergraduate senior level or beginning graduate level text for mathematical logic. There are virtually no prere quisites, although a familiarity with notions encountered in a beginning course in abstract algebra such as groups, rings, and fields will be useful in providing some motivation for the topics in Part III. An attempt has been made to develop the beginning of each part slowly and then to gradually quicken the pace and the complexity of the material. Each part ends with a brief introduction to selected topics of current interest. The text is divided into three parts: one dealing with set theory, another with computable function theory, and the last with model theory. Part III relies heavily on the notation, concepts and results discussed in Part I and to some extent on Part II. Parts I and II are independent of each other, and each provides enough material for a one semester course. The exercises cover a wide range of difficulty with an emphasis on more routine problems in the earlier sections of each part in order to familiarize the reader with the new notions and methods. The more difficult exercises are accompanied by hints. In some cases significant theorems are devel oped step by step with hints in the problems. Such theorems are not used later in the sequence.