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Structural Ramsey Theory of Metric Spaces and Topological Dynamics of Isometry Groups
L. Nguyen Van Thé, University of Calgary, AB, Canada

Memoirs of the American Mathematical Society
2010; 140 pp; softcover
Volume: 206
ISBN-10: 0-8218-4711-2
ISBN-13: 978-0-8218-4711-4
List Price: US$76
Individual Members: US$45.60
Institutional Members: US$60.80
Order Code: MEMO/206/968
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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.

Table of Contents

  • Introduction
  • Fraïssé classes of finite metric spaces and Urysohn spaces
  • Ramsey calculus, Ramsey degrees and universal minimal flows
  • Big Ramsey degrees, indivisibility and oscillation stability
  • Appendix A. Amalgamation classes \(\mathcal {M}_S\) when \(|S| \leqslant 4\)
  • Appendix B. Indivisibility of \(\mathbf {U}_S\) when \(|S| \leqslant 4\)
  • Appendix C. On the universal Urysohn space \(\mathbf {U}\)
  • Bibliography
  • Index
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