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Classical Descriptive Set Theory Book

Classical Descriptive Set Theory
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Classical Descriptive Set Theory, Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text presents a largely balanced approach to the subject, which combines many elements of the different traditions. It includes a wide variety of ex, Classical Descriptive Set Theory
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  • Classical Descriptive Set Theory
  • Written by author Alexander Kechris
  • Published by Springer-Verlag New York, LLC, 7/31/2012
  • Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text presents a largely balanced approach to the subject, which combines many elements of the different traditions. It includes a wide variety of ex
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Preface
Introduction
About This Book
Ch. I Polish Spaces 1
1 Topological and Metric Spaces 1
2 Trees 5
3 Polish Spaces 13
4 Compact Metrizable Spaces 18
5 Locally Compact Spaces 29
6 Perfect Polish Spaces 31
7 Zero-dimensional Spaces 35
8 Baire Category 41
9 Polish Groups 58
Ch. II Borel Sets 65
10 Measurable Spaces and Functions 65
11 Borel Sets and Functions 68
12 Standard Borel Spaces 73
13 Borel Sets as Clopen Sets 82
14 Analytic Sets and the Separation Theorem 85
15 Borel Injections and Isomorphisms 89
16 Borel Sets and Baire Category 94
17 Borel Sets and Measures 103
18 Uniformization Theorems 120
19 Partition Theorems 129
20 Borel Determinacy 137
21 Games People Play 149
22 The Borel Hierarchy 167
23 Some Examples 179
24 The Baire Hierarchy 190
Ch. III Analytic Sets 196
25 Representations of Analytic Sets 196
26 Universal and Complete Sets 205
27 Examples 209
28 Separation Theorems 217
29 Regularity Properties 226
30 Capacities 234
31 Analytic Well-founded Relations 239
Ch. IV Co-Analytic Sets 242
32 Review 242
33 Examples 245
34 Co-Analytic Ranks 267
35 Rank Theory 281
36 Scales and Uniformization 299
Ch. V Projective Sets 313
37 The Projective Hierarchy 313
38 Projective Determinacy 322
39 The Periodicity Theorems 327
40 Epilogue 346
Appendix A. Ordinals and Cardinals 349
Appendix B. Well-founded Relations 351
Appendix C. On Logical Notation 353
Notes and Hints 357
References 369
Symbols and Abbreviations 381
Index 387


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Classical Descriptive Set Theory, Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text presents a largely balanced approach to the subject, which combines many elements of the different traditions. It includes a wide variety of ex, Classical Descriptive Set Theory

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Classical Descriptive Set Theory, Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text presents a largely balanced approach to the subject, which combines many elements of the different traditions. It includes a wide variety of ex, Classical Descriptive Set Theory

Classical Descriptive Set Theory

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Classical Descriptive Set Theory, Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text presents a largely balanced approach to the subject, which combines many elements of the different traditions. It includes a wide variety of ex, Classical Descriptive Set Theory

Classical Descriptive Set Theory

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