Cover

Title

Copyright

TABLE OF CONTENTS

CHAPTER I: TOPOLOGICAL PRELIMINARIES

1.1 Notation

1.2 D-products

1.3 Compact Hausdorff spaces

1.4 Ordered spaces

1.5 D-limits

CHAPTER II: CONTINUOUS LOGICS

2.1 Definition of a continuous logic

2.2 Formulas

2.3 Two-valued logic

2.4 Sets of connectives and quantifiers

2.5 Examples

2.6 Some existence theorems

CHAPTER Ill: MODEL-THEORETIC PRELIMINARIES

3.1 Models

3.2 Truth values

3.3 The elementary topology

CHAPTER IV: ELEMENTARILY EQUIVALENT MODELS

4.1 The extended theory of a model

4.2 Elementary extensions

4.3 The downward Löwenheim-Skolem theorem

CHAPTER V: ULTRAPRODUCTS OF MODELS AND APPLICATIONS

5.1 The fundamental lemma

5.2 The compactness theorem

5.3 The upward Löwenheim-Skolem theorem

5.4 Good ultrafilters

5.5 Good ultra products

CHAPTER VI: SPECIAL MODELS

6.1 Saturated models

6.2 Existence of special models

6.3 Universal models

6.4 Uniqueness of special models

6.5 Some consequences of the generalized continuum hypothesis

CHAPTER VII: CLASSES PRESERVED UNDER ALGEBRAIC RELATIONS

7.1 The extended theory and order

7.2 Extensions of models and existential formulas

7.3 Homomorphisms and positive classes

7.4 Reduced products and conditional classes

HISTORICAL NOTES

BIBLIOGRAPHY

INDEX OF SYMBOLS

INDEX OF DEFINITIONS

INDEX OF EXERCISES