C. C. Chang and H. Jerome Keisler

Preface

1. Introduction

2. Models contructed from constants

3. Further model-theoretic constructions

4. Ultraproducts

5. Saturated and special models

6. More about ultraproducts and generalizations

7. Selected topics

Appendix A. Set theory

Appendix B. Open problems in classical model theory

Historical notes

References

Additional references

Index of definitions

Index of symbols

Model theory deals with a branch of mathematical logic showing connections between a formal language and its interpretations or models. This is the first and most successful textbook in logical model theory. Extensively updated and corrected in 1990 to accommodate developments in model theoretic methods — including classification theory and nonstandard analysis — the third edition added entirely new sections, exercises, and references.
Each chapter introduces an individual method and discusses specific applications. Basic methods of constructing models include constants, elementary chains, Skolem functions, indiscernibles, ultraproducts, and special models. The final chapters present more advanced topics that feature a combination of several methods. This classic treatment covers most aspects of first-order model theory and many of its applications to algebra and set theory.