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Classical Descriptive Set Theory : Graduate Texts in Mathematics - Alexander Kechris

Classical Descriptive Set Theory

Graduate Texts in Mathematics

Hardcover Published: 6th January 1995
ISBN: 9780387943749
Number Of Pages: 404

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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.

About This Book
Polish Spacesp. 1
Topological and Metric Spacesp. 1
Treesp. 5
Polish Spacesp. 13
Compact Metrizable Spacesp. 18
Locally Compact Spacesp. 29
Perfect Polish Spacesp. 31
Zero-dimensional Spacesp. 35
Baire Categoryp. 41
Polish Groupsp. 58
Borel Setsp. 65
Measurable Spaces and Functionsp. 65
Borel Sets and Functionsp. 68
Standard Borel Spacesp. 73
Borel Sets as Clopen Setsp. 82
Analytic Sets and the Separation Theoremp. 85
Borel Injections and Isomorphismsp. 89
Borel Sets and Baire Categoryp. 94
Borel Sets and Measuresp. 103
Uniformization Theoremsp. 120
Partition Theoremsp. 129
Borel Determinacyp. 137
Games People Playp. 149
The Borel Hierarchyp. 167
Some Examplesp. 179
The Baire Hierarchyp. 190
Analytic Setsp. 196
Representations of Analytic Setsp. 196
Universal and Complete Setsp. 205
Examplesp. 209
Separation Theoremsp. 217
Regularity Propertiesp. 226
Capacitiesp. 234
Analytic Well-founded Relationsp. 239
Co-Analytic Setsp. 242
Reviewp. 242
Examplesp. 245
Co-Analytic Ranksp. 267
Rank Theoryp. 281
Scales and Uniformizationp. 299
Projective Setsp. 313
The Projective Hierarchyp. 313
Projective Determinacyp. 322
The Periodicity Theoremsp. 327
Epiloguep. 346
Appendix A. Ordinals and Cardinalsp. 349
Appendix B. Well-founded Relationsp. 351
Appendix C. On Logical Notationp. 353
Notes and Hintsp. 357
Referencesp. 369
Symbols and Abbreviationsp. 381
Indexp. 387
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780387943749
ISBN-10: 0387943749
Series: Graduate Texts in Mathematics
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 404
Published: 6th January 1995
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.62 x 15.49  x 2.79
Weight (kg): 0.77

Earn 211 Qantas Points
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