| Preface Introduction About This Book CHAPTER. I Polish Spaces 1 Topological and Metric Spaces 2 Trees 3 Polish Spaces 4 Compact Metrizable Spaces 5 Locally Compact Spaces 6 Perfect Polish Spaces 7 Zero-dimensional Spaces 8 Baire Category 9 Polish Groups CHAPTER. II Borel Sets 10 Measurable Spaces and Functions 11 Borel Sets and Functions 12 Standard Borel Spaces 13 Borel Sets as Clopen Sets 14 Analytic Sets and the Separation Theorem 15 Borel Injections and Isomorphisms 16 Borel Sets and Baire Category 17 Borel Sets and Measures 18 Uniformization Theorems 19 Partition Theorems 20 Borel Determinacy 21 Games People Play 22 The Borel HierarCHAPTERy 23 Some Examples 24 The Baire HierarCHAPTERy CHAPTER. III Analytic Sets 25 Representations of Analytic Sets 26 Universal and Complete Sets 27 Examples 28 Separation Theorems 29 Regularity Properties 30 Capacities 31 Analytic Well-founded Relations CHAPTER. IV Co-Analytic Sets 32 Review 33 Examples 34 Co-Analytic Ranks 35 Rank Theory 36 Scales and Uniformization CHAPTER. V Projective Sets 37 The Projective HierarCHAPTERy 38 Projective Determinacy 39 The Periodicity Theorems 40 Epilogue Appendix A. Ordinals and Cardinals Appendix B. Well-founded Relations Appendix C. On Logical Notation Notes and Hints References Symbols and Abbreviations Index |
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