Author : Lou van den Dries
Publisher : Springer
Page : 201 pages
File Size : 43,19 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 : 37,54 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 : Deirdre Haskell
Publisher : Cambridge University Press
Page : 244 pages
File Size : 49,8 MB
Release : 2000-07-03
Category : Mathematics
ISBN : 9780521780681
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.
Author : Zoé Chatzidakis
Publisher : Cambridge University Press
Page : 0 pages
File Size : 26,89 MB
Release : 2008-05-22
Category : Mathematics
ISBN : 9780521694841
The first of a two-volume set showcasing the current research in model theory and its connections with number theory, algebraic geometry, real analytic geometry and differential algebra. This volume begins with 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 included showcase 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 two-volume set will undoubtedly appeal to all mathematicians with an interest in model theory and its applications.
Author : Zoé Maria Chatzidakis
Publisher : Cambridge University Press
Page : 5 pages
File Size : 19,93 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 : Alexander Prestel
Publisher : Springer Science & Business Media
Page : 198 pages
File Size : 12,21 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 : Luc Bélair
Publisher :
Page : 496 pages
File Size : 26,60 MB
Release : 2002
Category : Mathematics
ISBN :
Author :
Publisher :
Page : 0 pages
File Size : 32,69 MB
Release : 1973
Category : Model theory
ISBN : 9780720422009
Author : Katrin Tent
Publisher : Cambridge University Press
Page : 259 pages
File Size : 22,94 MB
Release : 2012-03-08
Category : Mathematics
ISBN : 052176324X
Concise introduction to current topics in model theory, including simple and stable theories.
Author : Jose Iovino
Publisher : CRC Press
Page : 382 pages
File Size : 35,3 MB
Release : 2017-08-14
Category : Mathematics
ISBN : 1315351099
Model theory is one of the central branches of mathematical logic. The field has evolved rapidly in the last few decades. This book is an introduction to current trends in model theory, and contains a collection of articles authored by top researchers in the field. It is intended as a reference for students as well as senior researchers.
