Classical Descriptive Set Theory

ISBN-10: 0387943749
ISBN-13: 9780387943749
Edition: 1995
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Description: 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  More...

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Book details

Copyright year: 1995
Publisher: Springer
Publication date: 1/6/1995
Binding: Hardcover
Pages: 404
Size: 6.50" wide x 9.75" long x 1.25" tall
Weight: 1.628
Language: English

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.

Preface
Introduction
About This Book
Polish Spaces
Topological and Metric Spaces
Trees
Polish Spaces
Compact Metrizable Spaces
Locally Compact Spaces
Perfect Polish Spaces
Zero-dimensional Spaces
Baire Category
Polish Groups
Borel Sets
Measurable Spaces and Functions
Borel Sets and Functions
Standard Borel Spaces
Borel Sets as Clopen Sets
Analytic Sets and the Separation Theorem
Borel Injections and Isomorphisms
Borel Sets and Baire Category
Borel Sets and Measures
Uniformization Theorems
Partition Theorems
Borel Determinacy
Games People Play
The Borel Hierarchy
Some Examples
The Baire Hierarchy
Analytic Sets
Representations of Analytic Sets
Universal and Complete Sets
Examples
Separation Theorems
Regularity Properties
Capacities
Analytic Well-founded Relations
Co-Analytic Sets
Review
Examples
Co-Analytic Ranks
Rank Theory
Scales and Uniformization
Projective Sets
The Projective Hierarchy
Projective Determinacy
The Periodicity Theorems
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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