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Classes of Polish Spaces Under Effective Borel Isomorphism
 
Vassilios Gregoriades Institut für Analysis und Algebra, Technische Universität Darmstadt, Germany
Front Cover for Classes of Polish Spaces Under Effective Borel Isomorphism
Available Formats:
Electronic ISBN: 978-1-4704-2822-8
Product Code: MEMO/240/1135.E
List Price: $79.00
MAA Member Price: $71.10
AMS Member Price: $47.40
Front Cover for Classes of Polish Spaces Under Effective Borel Isomorphism
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  • Front Cover for Classes of Polish Spaces Under Effective Borel Isomorphism
  • Back Cover for Classes of Polish Spaces Under Effective Borel Isomorphism
Classes of Polish Spaces Under Effective Borel Isomorphism
Vassilios Gregoriades Institut für Analysis und Algebra, Technische Universität Darmstadt, Germany
Available Formats:
Electronic ISBN:  978-1-4704-2822-8
Product Code:  MEMO/240/1135.E
List Price: $79.00
MAA Member Price: $71.10
AMS Member Price: $47.40
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2402015; 87 pp
    MSC: Primary 03;

    The author studies the equivalence classes under \(\Delta^1_1\) isomorphism, otherwise effective Borel isomorphism, between complete separable metric spaces which admit a recursive presentation and he shows the existence of strictly increasing and strictly decreasing sequences as well as of infinite antichains under the natural notion of \(\Delta^1_1\)-reduction, as opposed to the non-effective case, where only two such classes exist, the one of the Baire space and the one of the naturals.

  • Table of Contents
     
     
    • Chapters
    • Preface
    • 1. Introduction
    • 2. The spaces \ensuremath{\ensuremath{\mathcal{N}}^{T}}
    • 3. Kleene spaces
    • 4. Characterizations of \ensuremath{\mathcal{N}} up to \ensuremath{Δ^{1}_{1}} isomorphism
    • 5. Spector-Gandy spaces
    • 6. Questions and related results
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Volume: 2402015; 87 pp
MSC: Primary 03;

The author studies the equivalence classes under \(\Delta^1_1\) isomorphism, otherwise effective Borel isomorphism, between complete separable metric spaces which admit a recursive presentation and he shows the existence of strictly increasing and strictly decreasing sequences as well as of infinite antichains under the natural notion of \(\Delta^1_1\)-reduction, as opposed to the non-effective case, where only two such classes exist, the one of the Baire space and the one of the naturals.

  • Chapters
  • Preface
  • 1. Introduction
  • 2. The spaces \ensuremath{\ensuremath{\mathcal{N}}^{T}}
  • 3. Kleene spaces
  • 4. Characterizations of \ensuremath{\mathcal{N}} up to \ensuremath{Δ^{1}_{1}} isomorphism
  • 5. Spector-Gandy spaces
  • 6. Questions and related results
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