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Book Categories |
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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Add 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 to the inventory that you are selling on WonderClubX
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Add 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 to your collection on WonderClub |