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Mathematics | Model Theory : An Introduction

Model Theory : An Introduction

Series: Graduate Texts in Mathematics, Vol. 217

Marker, David

2002, VIII, 345 p.

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This book is a modern introduction to model theory which stresses applications to algebra throughout the text. The first half of the book includes classical material on model construction techniques, type spaces, prime models, saturated models, countable models, and indiscernibles and their applications. The author also includes an introduction to stability theory beginning with Morley's Categoricity Theorem and concentrating on omega-stable theories. One significant aspect of this text is the inclusion of chapters on important topics not covered in other introductory texts, such as omega-stable groups and the geometry of strongly minimal sets. The author then goes on to illustrate how these ingredients are used in Hrushovski's applications to diophantine geometry.

David Marker is Professor of Mathematics at the University of Illinois at Chicago. His main area of research involves mathematical logic and model theory, and their applications to algebra and geometry. This book was developed from a series of lectures given by the author at the Mathematical Sciences Research Institute in 1998.

Content Level » Graduate

Keywords » algebra - mathematical logic - model theory - set theory

Related subjects » Mathematics

Table of contents / Sample pages 

Introduction * Structures and Theories * Basic Techniques * Algebraic Examples * Realizing and Omitting Types * Indiscernibles * w-stable theoryes * w-stable groups * Geometry of strongly minmal sets * Appendix A: Set Theory * Appendix B: Real Algebra * References * Index

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