Classical Descriptive Set Theory

By: Alexander Kechris

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Hardcover | 6 January 1995

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428 Pages

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16.9 x 24.1 x 2.8

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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.

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Preface
Introduction
About This Book
Polish Spaces	p. 1
Topological and Metric Spaces	p. 1
Trees	p. 5
Polish Spaces	p. 13
Compact Metrizable Spaces	p. 18
Locally Compact Spaces	p. 29
Perfect Polish Spaces	p. 31
Zero-dimensional Spaces	p. 35
Baire Category	p. 41
Polish Groups	p. 58
Borel Sets	p. 65
Measurable Spaces and Functions	p. 65
Borel Sets and Functions	p. 68
Standard Borel Spaces	p. 73
Borel Sets as Clopen Sets	p. 82
Analytic Sets and the Separation Theorem	p. 85
Borel Injections and Isomorphisms	p. 89
Borel Sets and Baire Category	p. 94
Borel Sets and Measures	p. 103
Uniformization Theorems	p. 120
Partition Theorems	p. 129
Borel Determinacy	p. 137
Games People Play	p. 149
The Borel Hierarchy	p. 167
Some Examples	p. 179
The Baire Hierarchy	p. 190
Analytic Sets	p. 196
Representations of Analytic Sets	p. 196
Universal and Complete Sets	p. 205
Examples	p. 209
Separation Theorems	p. 217
Regularity Properties	p. 226
Capacities	p. 234
Analytic Well-founded Relations	p. 239
Co-Analytic Sets	p. 242
Review	p. 242
Examples	p. 245
Co-Analytic Ranks	p. 267
Rank Theory	p. 281
Scales and Uniformization	p. 299
Projective Sets	p. 313
The Projective Hierarchy	p. 313
Projective Determinacy	p. 322
The Periodicity Theorems	p. 327
Epilogue	p. 346
Appendix A. Ordinals and Cardinals	p. 349
Appendix B. Well-founded Relations	p. 351
Appendix C. On Logical Notation	p. 353
Notes and Hints	p. 357
References	p. 369
Symbols and Abbreviations	p. 381
Index	p. 387
Table of Contents provided by Blackwell. All Rights Reserved.

Classical Descriptive Set Theory

At a Glance

Hardcover

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