Model Theory by Chang, C.C. -- Read -- Imperial Library of Trantor

Index

Cover Title Page Copyright Page Preface to the Dover Edition Preface How to use this book as a Text Contents Chapter 1. Introduction

1.1.What is model theory? 1.2.Model theory for sentential logic 1.3.Languages, models and satisfaction 1.4.Theories and examples of theories 1.5.Elimination of quantifiers

Chapter 2. Models constructed from constants

2.1.Completeness and compactness 2.2.Refinements of the method. Omitting types and interpolation theorems 2.3.Countable models of complete theories 2.4.Recursively saturated models 2.5.Lindstros characterization of first order logic

Chapter 3. Further model-theoretic constructions

3.1.Elementary extensions and elementary chains 3.2.Applications of elementary chains 3.3.Skolem functions and indiscernibles 3.4.Some examples 3.5.Model completeness

Chapter 4. Ultraproducts

4.1.The fundamental theorem 4.2.Measurable cardinals 4.3.Regular ultrapowers 4.4.Nonstandard universes

Chapter 5. Saturated and special models

5.1.Saturated and special models 5.2.Preservation theorems 5.3.Applications of special models to the theory of definability 5.4.Applications to field theory 5.5.Application to Boolean algebras

Chapter 6. More about ultraproducts and generalizations

6.1.Ultraproducts which are saturated 6.2.Direct products, reduced products, and Horn sentences 6.3.Direct products, reduced products, and Horn sentences (continued) 6.4.Limit ultrapowers and complete extensions 6.5.Iterated ultrapowers

Chapter 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