Model Theory

An Introduction

  • David Marker

Part of the Graduate Texts in Mathematics book series (GTM, volume 217)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Pages 1-6
  3. Pages 33-69
  4. Pages 71-113
  5. Pages 175-205
  6. Pages 207-249
  7. Pages 251-288
  8. Back Matter
    Pages 315-342

About this book

Introduction

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.

Keywords

algebra mathematical logic model theory set theory

Authors and affiliations

  • David Marker
    • 1
  1. 1.Department of MathematicsUniversity of IllinoisChicagoUSA

Bibliographic information

  • DOI https://doi.org/10.1007/b98860
  • Copyright Information Springer-Verlag New York, Inc. 2002
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-98760-6
  • Online ISBN 978-0-387-22734-4
  • Series Print ISSN 0072-5285
  • About this book