Electronic ISBN:  9781470428228 
Product Code:  MEMO/240/1135.E 
87 pp 
List Price:  $79.00 
MAA Member Price:  $71.10 
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 240; 2015MSC: 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 noneffective 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. SpectorGandy spaces

6. Questions and related results


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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 noneffective 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. SpectorGandy spaces

6. Questions and related results