Divisibility of countable metric spaces

DOI10.1016/j.ejc.2006.06.024zbMath1206.54025arXivmath/0510254OpenAlexW2121495542MaRDI QIDQ2372435

Christian Delhommé, Maurice Pouzet, Claude Laflamme, Norbert W. Sauer

Publication date: 27 July 2007

Published in: European Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0510254

zbMATH Keywords

boundedUrysohn spaceultrametric spacesindivisible metric spacepartitions of countable metric spacestotally Cantor disconnected

Mathematics Subject Classification ID

Metric spaces, metrizability (54E35) Model theory of finite structures (03C13) Ramsey theory (05D10) Properties of classes of models (03C52) Partition relations (03E02) Basic properties of first-order languages and structures (03C07)

Related Items (29)

A universal separable diversity ⋮ Choiceless Ramsey theory of linear orders ⋮ Hereditary properties of finite ultrametric spaces ⋮ Age and weak indivisibility ⋮ ON PRODUCTS OF ELEMENTARILY INDIVISIBLE STRUCTURES ⋮ Extending partial isometries of generalized metric spaces ⋮ Vertex partitions of metric spaces with finite distance sets ⋮ Indivisible ultrametric spaces ⋮ A finite presentation of the rational Urysohn space ⋮ The oscillation stability problem for the Urysohn sphere: a combinatorial approach ⋮ A theorem of Hrushovski-Solecki-Vershik applied to uniform and coarse embeddings of the Urysohn metric space ⋮ Polish groups and Baire category methods ⋮ Neostability in countable homogeneous metric spaces ⋮ Structural Ramsey theory of metric spaces and topological dynamics of isometry groups ⋮ Polish metric spaces with fixed distance set ⋮ Finite big Ramsey degrees in universal structures ⋮ Some weak indivisibility results in ultrahomogeneous metric spaces ⋮ Distance structures for generalized metric spaces ⋮ Simplicity of the automorphism groups of generalised metric spaces ⋮ DISCRETE METRIC SPACES: STRUCTURE, ENUMERATION, AND 0-1 LAWS ⋮ Representation of ideals of relational structures ⋮ Conant's generalised metric spaces are Ramsey ⋮ The Urysohn sphere is oscillation stable ⋮ Locally Roelcke precompact Polish groups ⋮ All those Ramsey classes (Ramsey classes with closures and forbidden homomorphisms) ⋮ Cohen-like first order structures ⋮ Distinguishing number of universal homogeneous Urysohn metric spaces ⋮ Unnamed Item ⋮ The Complexity of Network Satisfaction Problems for Symmetric Relation Algebras with a Flexible Atom

Cites Work

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• Ramsey varieties
• Indivisible ultrametric spaces
• An oscillation theorem for groups of isometries
• Ramsey properties for classes of relational systems
• Theory of relations. Transl. from the French by P. Clote. With an appendix by Norbert Sauer.
• Indivisible homogeneous directed graphs and a game for vertex partitions
• Ubiquity in category for metric spaces and transition systems
• The category of ultrametric spaces is isomorphic to the category of complete, atomic, tree-like, and real graduated lattices LAT\(^*\)
• Big Ramsey Degrees and Divisibility in Classes of Ultrametric Spaces
• Regularity and Positional Games
• Canonical Vertex Partitions
• On ultrametrization of general metric spaces
• Concerning similarity transformations of linearly ordered sets

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