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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 Click above image for expanded view 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.

• 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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