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 : 2000-10-31
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 2000-10-31 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.
Mathematical Logic And Model Theory
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Author : Alexander Prestel
language : en
Publisher: Springer
Release Date : 2011-08-27
Mathematical Logic And Model Theory written by Alexander Prestel and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-27 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.
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.
Can we reproduce the inimitable, or give a new life to what has been af fected by the weariness of existence? Folks, what you have in your hands is a translation into English of a book that was first published in 1985 by its author, that is, myself, at the end of an editorial adventure about which you will find some details later. It was written in a dialect of Latin that is spoken as a native language in some parts of Europe, Canada, the U. S. A. , the West Indies, and is used as a language of communication between several countries in Africa. It is also sometimes used as a lan guage of communication between the members of a much more restricted community: mathematicians. This translation is indeed quite a faithful rendering of the original: Only a final section, on the reals, has been added to Chapter 6, plus a few notes now and then. On the title page you see an inscription in Arabic letters, with a transcription in the Latin (some poorly informed people say English!) alphabet below; I designed the calligraphy myself.
A First Course In Logic
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Author : Shawn Hedman
language : en
Publisher: OUP Oxford
Release Date : 2004-07-08
A First Course In Logic written by Shawn Hedman and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-07-08 with Mathematics categories.
The ability to reason and think in a logical manner forms the basis of learning for most mathematics, computer science, philosophy and logic students. Based on the author's teaching notes at the University of Maryland and aimed at a broad audience, this text covers the fundamental topics in classical logic in an extremely clear, thorough and accurate style that is accessible to all the above. Covering propositional logic, first-order logic, and second-order logic, as well as proof theory, computability theory, and model theory, the text also contains numerous carefully graded exercises and is ideal for a first or refresher course.
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.
Introduction To Model Theory And To The Metamathematics Of Algebra
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Author : Abraham Robinson
language : en
Publisher:
Release Date : 1974
Introduction To Model Theory And To The Metamathematics Of Algebra written by Abraham Robinson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Algebra categories.
Model Theory Algebra And Geometry
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Author : Deirdre Haskell
language : en
Publisher: Cambridge University Press
Release Date : 2000-07-03
Model Theory Algebra And Geometry written by Deirdre Haskell 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 2000-07-03 with Mathematics categories.
Model theory has made substantial contributions to semialgebraic, subanalytic, p-adic, rigid and diophantine geometry. These applications range from a proof of the rationality of certain Poincare series associated to varieties over p-adic fields, to a proof of the Mordell-Lang conjecture for function fields in positive characteristic. In some cases (such as the latter) it is the most abstract aspects of model theory which are relevant. This book, originally published in 2000, arising from a series of introductory lectures for graduate students, provides the necessary background to understanding both the model theory and the mathematics behind these applications. The book is unique in that the whole spectrum of contemporary model theory (stability, simplicity, o-minimality and variations) is covered and diverse areas of geometry (algebraic, diophantine, real analytic, p-adic, and rigid) are introduced and discussed, all by leading experts in their fields.
Model Theory And Applications
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Author : O.V. Belegradek
language : en
Publisher: American Mathematical Soc.
Release Date :
Model Theory And Applications written by O.V. Belegradek 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.
This volume is a collection of papers on model theory and its applications. The longest paper, "Model Theory of Unitriangular Groups" by O. V. Belegradek, forms a subtle general theory behind Mal'tsev's famous correspondence between rings and groups. This is the first published paper on the topic. Given the present model-theoretic interest in algebraic groups, Belegradek's work is of particular interest to logicians and algebraists. The rest of the collection consists of papers on various questions of model theory, mainly on stability theory. Contributors are leading Russian researchers in the field.
Introduction To Model Theory And To The Metamathematics Of Algebra
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Author : Abraham Robinson
language : en
Publisher:
Release Date : 1974
Introduction To Model Theory And To The Metamathematics Of Algebra written by Abraham Robinson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with categories.