Author : Lou van den Dries
Publisher : Springer
Page : 201 pages
File Size : 37,26 MB
Release : 2014-09-20
Category : Mathematics
ISBN : 3642549365
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 : David Marker
Publisher : Springer Science & Business Media
Page : 342 pages
File Size : 18,16 MB
Release : 2006-04-06
Category : Mathematics
ISBN : 0387227342
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 : Alexander Prestel
Publisher : Springer Science & Business Media
Page : 198 pages
File Size : 27,12 MB
Release : 2011-08-21
Category : Mathematics
ISBN : 1447121767
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.
Author : Katrin Tent
Publisher : Cambridge University Press
Page : 259 pages
File Size : 45,97 MB
Release : 2012-03-08
Category : Mathematics
ISBN : 052176324X
Concise introduction to current topics in model theory, including simple and stable theories.
Author : Zoé Maria Chatzidakis
Publisher : Cambridge University Press
Page : 5 pages
File Size : 42,66 MB
Release : 2008
Category : Algebra, Homological
ISBN : 0521709083
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 : W. A. J. Luxemburg
Publisher :
Page : 328 pages
File Size : 27,45 MB
Release : 1969
Category : Mathematics
ISBN :
Author : Deirdre Haskell
Publisher : Cambridge University Press
Page : 244 pages
File Size : 16,43 MB
Release : 2000-07-03
Category : Mathematics
ISBN : 9780521780681
Leading experts survey the connections between model theory and semialgebraic, subanalytic, p-adic, rigid and diophantine geometry.
Author : Alexander Martsinkovsky
Publisher : Springer Nature
Page : 256 pages
File Size : 12,66 MB
Release :
Category :
ISBN : 3031530632
Author : Chen Chung Chang
Publisher : North-Holland
Page : 584 pages
File Size : 14,4 MB
Release : 1977
Category : Mathematics
ISBN :
Since the second edition of this book (1977), Model Theory has changed radically, and is now concerned with fields such as classification (or stability) theory, nonstandard analysis, model-theoretic algebra, recursive model theory, abstract model theory, and model theories for a host of nonfirst order logics. Model theoretic methods have also had a major impact on set theory, recursion theory, and proof theory. This new edition has been updated to take account of these changes, while preserving its usefulness as a first textbook in model theory. Whole new sections have been added, as well as new exercises and references. A number of updates, improvements and corrections have been made to the main text.
Author : Annalisa Marcja
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 36,76 MB
Release : 2003
Category : Mathematics
ISBN : 9781402013300
Since its birth, Model Theory has been developing a number of methods and concepts that have their intrinsic relevance, but also provide fruitful and notable applications in various fields of Mathematics. It is a lively and fertile research area which deserves the attention of the mathematical world. This volume-is easily accessible to young people and mathematicians unfamiliar with logic; -gives a terse historical picture of Model Theory; -introduces the latest developments in the area; -provides 'hands-on' proofs of elimination of quantifiers, elimination of imaginaries and other relevant matters. A Guide to Classical and Modern Model Theory is for trainees and professional model theorists, mathematicians working in Algebra and Geometry and young people with a basic knowledge of logic.
