[PDF] Model Theory With Applications To Algebra And Analysis eBook

Author : Lou van den Dries
Publisher : Springer
Page : 201 pages
File Size : 37,47 MB
Release : 2014-09-20
Category : Mathematics
ISBN : 3642549365

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Presenting recent developments and applications, the book focuses on four main topics in current model theory: 1) the model theory of valued fields; 2) undecidability in arithmetic; 3) NIP theories; and 4) the model theory of real and complex exponentiation. Young researchers in model theory will particularly benefit from the book, as will more senior researchers in other branches of mathematics.

Author : Zoé Chatzidakis
Publisher : Cambridge University Press
Page : 0 pages
File Size : 48,97 MB
Release : 2008-05-22
Category : Mathematics
ISBN : 9781107048867

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The first of a two volume set showcasing current research in model theory and its connections with number theory, algebraic geometry, real analytic geometry and differential algebra. Each volume contains a series of expository essays and research papers around the subject matter of a Newton Institute Semester on Model Theory and Applications to Algebra and Analysis. The articles convey outstanding new research on topics such as model theory and conjectures around Mordell-Lang; arithmetic of differential equations, and Galois theory of difference equations; model theory and complex analytic geometry; o-minimality; model theory and noncommutative geometry; definable groups of finite dimension; Hilbert's tenth problem; and Hrushovski constructions. With contributions from so many leaders in the field, this book will undoubtedly appeal to all mathematicians with an interest in model theory and its applications, from graduate students to senior researchers and from beginners to experts.

Author : Zoé Chatzidakis
Publisher : Cambridge University Press
Page : 444 pages
File Size : 28,79 MB
Release : 2008-05-22
Category : Mathematics
ISBN : 9780521709088

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The second of a two-volume set showcasing current research in model theory and its connections with number theory, algebraic geometry, real analytic geometry and differential algebra. This volume completes a series of expository essays and research papers around the subject matter of a Newton Institute Semester on Model Theory and Applications to Algebra and Analysis. The articles concluded here reveal new research on topics such as model theory and conjectures around Mordell-Lang; arithmetic of differential equations, and Galois Theory of difference equations; model theory and complex analytic geometry; o-minimality; model theory and non-commutative geometry; definable groups of finite dimension; Hilbert's tenth problem; and Hrushovski constructions. With contributions from so many leaders in the field, this two-volume set will undoubtedly appeal to all mathematicians with an interest in model theory and its applications.

Author : Christian.U Jensen
Publisher : Routledge
Page : 464 pages
File Size : 12,26 MB
Release : 2022-03-11
Category : Mathematics
ISBN : 1351431129

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This volume highlights the links between model theory and algebra. The work contains a definitive account of algebraically compact modules, a topic of central importance for both module and model theory. Using concrete examples, particular emphasis is given to model theoretic concepts, such as axiomizability. Pure mathematicians, especially algebraists, ring theorists, logicians, model theorists and representation theorists, should find this an absorbing and stimulating book.

Author : Zoé Maria Chatzidakis
Publisher :
Page : 352 pages
File Size : 11,95 MB
Release : 2014-05-14
Category : MATHEMATICS
ISBN : 9781107362949

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Account of current research in model theory and its connections with algebra and analysis; contributions from leaders in the field.

Author : David Marker
Publisher : Springer Science & Business Media
Page : 342 pages
File Size : 22,71 MB
Release : 2006-04-06
Category : Mathematics
ISBN : 0387227342

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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

Author : Jonathan Kirby
Publisher : Cambridge University Press
Page : 197 pages
File Size : 42,73 MB
Release : 2019-04-18
Category : Mathematics
ISBN : 1316732398

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Model theory begins with an audacious idea: to consider statements about mathematical structures as mathematical objects of study in their own right. While inherently important as a tool of mathematical logic, it also enjoys connections to and applications in diverse branches of mathematics, including algebra, number theory and analysis. Despite this, traditional introductions to model theory assume a graduate-level background of the reader. In this innovative textbook, Jonathan Kirby brings model theory to an undergraduate audience. The highlights of basic model theory are illustrated through examples from specific structures familiar from undergraduate mathematics, paying particular attention to definable sets throughout. With numerous exercises of varying difficulty, this is an accessible introduction to model theory and its place in mathematics.

Author : Alexander Prestel
Publisher : Springer Science & Business Media
Page : 198 pages
File Size : 24,66 MB
Release : 2011-08-21
Category : Mathematics
ISBN : 1447121767

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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.