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Classes of Polish Spaces Under Effective Borel Isomorphism
 
Vassilios Gregoriades Institut für Analysis und Algebra, Technische Universität Darmstadt, Germany
Classes of Polish Spaces Under Effective Borel Isomorphism
eBook 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
Classes of Polish Spaces Under Effective Borel Isomorphism
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Classes of Polish Spaces Under Effective Borel Isomorphism
Vassilios Gregoriades Institut für Analysis und Algebra, Technische Universität Darmstadt, Germany
eBook 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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