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Ultraproducts in Analysis&by C.Ward Henson and Jose Iovino 1

1 Introduction 3

2 Normed Space Structures 10

3 Signatures 13

4 Ultrapowers of Normed Space Structures 17

5 Positive Bounded Formulas 21

6 Basic Model Theory Ⅰ 31

7 Quantifier-Free Formulas 34

8 Ultraproducts of Normed Space Structures 38

9 Basic Model Theory Ⅱ 43

10 Isomorphic Ultrapowers 55

11 Alternative Formulations of the Theory 72

12 Homogeneous Structures 75

13 More Model Theory 79

14 Types 96

References 107

Index of Notation 111

Index 112

Actions of Polish Groups and Classification Problems&by Alexander S.Kechris 115

1 Introduction 117

2 The General Glimm-Effros Dichotomy 120

3 Actions of Polish Groups 123

4 Actions of Countable Groups 126

5 Actions of Locally Compact Groups 131

6 Actions of the Infinite Symmetric Group 133

7 Turbulence Ⅰ：Overview 137

8 Turbulence Ⅱ：Basic Facts 143

9 Turbulence Ⅲ：Induced Actions 146

10 Turbulence Ⅳ：Some Examples 150

11 Turbulence Ⅴ：Calmness 152

12 Turbulence Ⅵ：The First Main Theorem 157

13 Turbulence Ⅶ：The Second Main Theorem 163

References 183

Index 186

On Subspaces，Asymptotic Structure，and Distortion of Banach Spaces； Connections with Logic&by Edward Odell 189

1 Introduction 191

2 Background material：The 60’s and 70’s 194

3 The unconditional basic sequence problem and connections with distortion 208

4 Gowers’ dichotomy：A block Ramsey Theorem 217

5 Distortion 223

6 Asymptotic structure 233

7 Ordinal Indices 244

8 The homogeneous Banach space problem 252

9 Concluding remarks 254

References 256

Index 265