A Shorter Model Theory

Author: Wilfrid Hodges
Publisher: Cambridge University Press
ISBN: 9780521587136
Category : Mathematics
Languages : en
Pages : 322

Book Description
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.

An Invitation to Model Theory

Author: Jonathan Kirby
Publisher: Cambridge University Press
ISBN: 1316732398
Category : Mathematics
Languages : en
Pages : 197

Book Description
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.

Model Theory : An Introduction

Author: David Marker
Publisher: Springer Science & Business Media
ISBN: 0387227342
Category : Mathematics
Languages : en
Pages : 342

Book Description
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

Model Theory

Author:
Publisher:
ISBN: 9780720422009
Category : Model theory
Languages : en
Pages : 0

Book Description

Model Theory and the Philosophy of Mathematical Practice

Author: John T. Baldwin
Publisher: Cambridge University Press
ISBN: 1107189217
Category : Mathematics
Languages : en
Pages : 365

Book Description
Recounts the modern transformation of model theory and its effects on the philosophy of mathematics and mathematical practice.

A Course in Model Theory

Author: Bruno Poizat
Publisher: Springer Science & Business Media
ISBN: 1441986227
Category : Mathematics
Languages : en
Pages : 472

Book Description
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.

Elements of Finite Model Theory

Author: Leonid Libkin
Publisher: Springer Science & Business Media
ISBN: 3662070030
Category : Mathematics
Languages : en
Pages : 320

Book Description
Emphasizes the computer science aspects of the subject. Details applications in databases, complexity theory, and formal languages, as well as other branches of computer science.

A Course in Model Theory

Author: Katrin Tent
Publisher: Cambridge University Press
ISBN: 052176324X
Category : Mathematics
Languages : en
Pages : 259

Book Description
Concise introduction to current topics in model theory, including simple and stable theories.

Classification Theory

Author: S. Shelah
Publisher: Elsevier
ISBN: 008088024X
Category : Computers
Languages : en
Pages : 741

Book Description
In this research monograph, the author's work on classification and related topics are presented. This revised edition brings the book up to date with the addition of four new chapters as well as various corrections to the 1978 text. The additional chapters X - XIII present the solution to countable first order T of what the author sees as the main test of the theory. In Chapter X the Dimensional Order Property is introduced and it is shown to be a meaningful dividing line for superstable theories. In Chapter XI there is a proof of the decomposition theorems. Chapter XII is the crux of the matter: there is proof that the negation of the assumption used in Chapter XI implies that in models of T a relation can be defined which orders a large subset of m

Mathematical Logic and Model Theory

Author: Alexander Prestel
Publisher: Springer Science & Business Media
ISBN: 1447121767
Category : Mathematics
Languages : en
Pages : 198

Book Description
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.