Contents

pp vii-viii

Preface

pp ix-x

Introduction

pp xi-xiv

Part One: Ultraproducts in Analysis

pp 1-2

1 - Introduction

pp 3-9

2 - Normed Space Structures

pp 10-12

3 - Signatures

pp 13-16

4 - Ultrapowers of Normed Space Structures

pp 17-20

5 - Positive Bounded Formulas

pp 21-30

Basic Model Theory I

pp 31-33

7 - Quantifier-Free Formulas

pp 34-37

8 - Ultraproducts of Normed Space Structures

pp 38-42

9 - Basic Model Theory II

pp 43-54

10 - Isomorphic Ultrapowers

pp 55-71

11 - Alternative Formulations of the Theory

pp 72-74

12 - Homogeneous Structures

pp 75-78

13 - More Model Theory

pp 79-95

14 - Types

pp 96-106

References

pp 107-110

Index of Notation

pp 111-111

Index

pp 112-114

Actions of Polish Groups and Classification Problems

pp 115-116

1 - Introduction

pp 117-119

2 - The General Glimm-Effros Dichotomy

pp 120-122

3 - Actions of Polish Groups

pp 123-125

4 - Actions of Countable Groups

pp 126-130

5 - Actions of Locally Compact Groups

pp 131-132

6 - Actions of the Infinite Symmetric Group

pp 133-136

7 - Turbulence I: Overview

pp 137-142