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Classical Descriptive Set Theory

  • Textbook
  • © 1995

Overview

Authors:
  1. Alexander S. Kechris

    1. Alfred P. Sloan Laboratory of Mathematics and Physics Mathematics 253-37, California Institute of Technology, Pasadena, USA

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Part of the book series: Graduate Texts in Mathematics (GTM, volume 156)

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Table of contents (40 chapters)

  1. Front Matter

    Pages i-xviii
    Download chapter PDF

  2. Polish Spaces

    1. Topological and Metric Spaces

      • Alexander S. Kechris
      Pages 1-4

    2. Trees

      • Alexander S. Kechris
      Pages 5-12

    3. Polish Spaces

      • Alexander S. Kechris
      Pages 13-17

    4. Compact Metrizable Spaces

      • Alexander S. Kechris
      Pages 18-28

    5. Locally Compact Spaces

      • Alexander S. Kechris
      Pages 29-30

    6. Perfect Polish Spaces

      • Alexander S. Kechris
      Pages 31-34

    7. Zero-dimensional Spaces

      • Alexander S. Kechris
      Pages 35-40

    8. Baire Category

      • Alexander S. Kechris
      Pages 41-57

    9. Polish Groups

      • Alexander S. Kechris
      Pages 58-64

  3. Borel Sets

    1. Measurable Spaces and Functions

      • Alexander S. Kechris
      Pages 65-67

    2. Borel Sets and Functions

      • Alexander S. Kechris
      Pages 68-72

    3. Standard Borel Spaces

      • Alexander S. Kechris
      Pages 73-81

    4. Borel Sets as Clopen Sets

      • Alexander S. Kechris
      Pages 82-84

    5. Analytic Sets and the Separation Theorem

      • Alexander S. Kechris
      Pages 85-88

    6. Borel Injections and Isomorphisms

      • Alexander S. Kechris
      Pages 89-93

    7. Borel Sets and Baire Category

      • Alexander S. Kechris
      Pages 94-102

    8. Borel Sets and Measures

      • Alexander S. Kechris
      Pages 103-119

    9. Uniformization Theorems

      • Alexander S. Kechris
      Pages 120-128

    10. Partition Theorems

      • Alexander S. Kechris
      Pages 129-136
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Keywords

About this book

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.

Authors and Affiliations

  • Alfred P. Sloan Laboratory of Mathematics and Physics Mathematics 253-37, California Institute of Technology, Pasadena, USA

    Alexander S. Kechris

Bibliographic Information

  • Book Title: Classical Descriptive Set Theory

  • Authors: Alexander S. Kechris

  • Series Title: Graduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-4190-4

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1995

  • Hardcover ISBN: 978-0-387-94374-9Published: 06 January 1995

  • Softcover ISBN: 978-1-4612-8692-9Published: 21 December 2011

  • eBook ISBN: 978-1-4612-4190-4Published: 06 December 2012

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 1

  • Number of Pages: XVIII, 404

  • Topics: Mathematical Logic and Foundations, Topology

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