Classical descriptive set theory经典描述性集合论
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作者： Alexander S. Kechris著
出 版 社：
出版时间： 1995-1-1字数：版次： 1页数： 402印刷时间： 1995/01/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9780387943749包装： 精装内容简介
Descriptive set theory has been one of the main areas of research in set theory for almost a century. This text attempts to present a largely balanced approach, which combines many elements of the different traditions of the subject. It includes a wide variety of examples, exercises (over 400), and applications, in order to illustrate the general concepts and results of the theory.
This text provides a first basic course in classical descriptive set theory and covers material with which mathematicians interested in the subject for its own sake or those that wish to use it in their field should be familiar. Over the years, researchers in diverse areas of mathematics, such as logic and set theory, analysis, topology, probability theory, etc., have brought to the subject of descriptive set theory their own intuitions, concepts, terminology and notation.
目录
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
