A Course in Model Theory

This concise introduction to model theory begins with standard notions and takes the reader through to more advanced topics such as stability, simplicity and Hrushovski constructions. The authors introduce the classic results, as well as more recent developments in this vibrant area of mathematical logic. Concrete mathematical examples are included throughout to make the concepts easier to follow. The book also contains over 200 exercises, many with solutions, making the book a useful resource for graduate students as well as researchers.

Review

“This is a concise and elegant introduction to modern model theory. It is remarkable that within 184 pages of the main text and without assuming any background in logic, the authors take the reader from the classical parts of the subject, such as the compactness theorem and quantifier elimination, through Morley’s Theorem and then onwards tot eh more recent developments of stability theory and forking.

David Evans, Mathematical Reviews

Book Description

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

Table of Contents

Chapter 1 THE BASICS

Chapter 2 ELEMENTARY EXTENSIONS AND COMPACTNESS

Chapter 3 QUANTIFIER ELIMINATION

Chapter 4 COUNTABLE MODELS

Chapter 5 CATEGORICAL THEORIES

Chapter 6 MORLEY RANK

Chapter 7 SIMPLE THEORIES

Chapter 8 STABLE THEORIES

Chapter 9 PRIME EXTENSIONS

Chapter 10 THE FINE STRUCTURE OF CATEGORICAL THEORIES

Appendix A SET THEORY

Appendix B FIELDS

Appendix C COMBINATORICS

Appendix D SOLUTIONS TO EXERCISES

About the Authors

Katrin Tent is Professor of Mathematics at Westfälische Wilhelms-Universität Münster, Germany.

Martin Ziegler is a Professor of Mathematics at Albert-Ludwigs-Universität Freiburg, Germany.