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Structural Ramsey Theory of Metric Spaces and Topological Dynamics of Isometry Groups
| eBook ISBN: | 978-1-4704-0582-3 |
| Product Code: | MEMO/206/968.E |
| List Price: | $76.00 |
| MAA Member Price: | $68.40 |
| AMS Member Price: | $45.60 |
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Structural Ramsey Theory of Metric Spaces and Topological Dynamics of Isometry Groups
| eBook ISBN: | 978-1-4704-0582-3 |
| Product Code: | MEMO/206/968.E |
| List Price: | $76.00 |
| MAA Member Price: | $68.40 |
| AMS Member Price: | $45.60 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 206; 2010; 140 ppMSC: Primary 03; Secondary 05; 22
In 2003, Kechris, Pestov and Todorcevic showed that the structure of certain separable metric spaces—called ultrahomogeneous—is closely related to the combinatorial behavior of the class of their finite metric spaces. The purpose of the present paper is to explore different aspects of this connection.
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Table of Contents
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Chapters
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Preamble
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Preliminary remarks
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Introduction
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1. Fraïssé classes of finite metric spaces and Urysohn spaces
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2. Ramsey calculus, Ramsey degrees and universal minimal flows
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3. Big Ramsey degrees, indivisibility and oscillation stability
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Appendix A. Amalgamation classes $\mathcal {M}_S$ when $|S| \leqslant 4$
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Appendix B. Indivisibility of $\textbf {U}_S$ when $|S| \leqslant 4$
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Appendix C. On the universal Urysohn space $\textbf {U}$
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
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Volume: 206; 2010; 140 pp
MSC: Primary 03; Secondary 05; 22
In 2003, Kechris, Pestov and Todorcevic showed that the structure of certain separable metric spaces—called ultrahomogeneous—is closely related to the combinatorial behavior of the class of their finite metric spaces. The purpose of the present paper is to explore different aspects of this connection.
-
Chapters
-
Preamble
-
Preliminary remarks
-
Introduction
-
1. Fraïssé classes of finite metric spaces and Urysohn spaces
-
2. Ramsey calculus, Ramsey degrees and universal minimal flows
-
3. Big Ramsey degrees, indivisibility and oscillation stability
-
Appendix A. Amalgamation classes $\mathcal {M}_S$ when $|S| \leqslant 4$
-
Appendix B. Indivisibility of $\textbf {U}_S$ when $|S| \leqslant 4$
-
Appendix C. On the universal Urysohn space $\textbf {U}$
Review Copy – for publishers of book reviews
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