Structural Ramsey theory of metric spaces and topological dynamics of isometry groups

DOI10.1090/S0065-9266-10-00586-7zbMath1203.05159arXiv0804.1593OpenAlexW4245310088MaRDI QIDQ3578251

Lionel Nguyen Van Thé

Publication date: 15 July 2010

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0804.1593

zbMATH Keywords

Ramsey theorymetric geometryUrysohn metric spaceextreme amenabilityFraïssé theoryoscillation stabilitytopological group actionsuniversal minimal flows

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to combinatorics (05-02) Structure of general topological groups (22A05) Metric spaces, metrizability (54E35) Generalized Ramsey theory (05C55) Ramsey theory (05D10) Research exposition (monographs, survey articles) pertaining to topological groups (22-02) Partition relations (03E02) Research exposition (monographs, survey articles) pertaining to general topology (54-02) General theory of group and pseudogroup actions (22F05)

Related Items (28)

Ramsey degrees, labeled and unlabeled partitions ⋮ Galvin’s problem in higher dimensions ⋮ A Ramsey class for Steiner systems ⋮ A universal separable diversity ⋮ Unary functions ⋮ Polish ultrametric Urysohn spaces and their isometry groups ⋮ Categorical view of the partite lemma in structural Ramsey theory ⋮ Constructions of Urysohn universal ultrametric spaces ⋮ Uniqueness and homogeneity of non-separable Urysohn universal ultrametric spaces ⋮ Forcing with copies of the Rado and Henson graphs ⋮ Dual Ramsey properties for classes of algebras ⋮ Subgroups of isometries of Urysohn-Katětov metric spaces of uncountable density ⋮ The independence of Stone’s Theorem from the Boolean Prime Ideal Theorem ⋮ Generic dynamics on compact metric spaces ⋮ Vertex partitions of metric spaces with finite distance sets ⋮ Random orderings and unique ergodicity of automorphism groups ⋮ Pre-adjunctions and the Ramsey property ⋮ Directed graphs and boron trees ⋮ Universal Flows of Closed Subgroups of S ∞ and Relative Extreme Amenability ⋮ Some weak indivisibility results in ultrahomogeneous metric spaces ⋮ Distance structures for generalized metric spaces ⋮ Binary simple homogeneous structures ⋮ Scott rank of Polish metric spaces ⋮ Conant's generalised metric spaces are Ramsey ⋮ Fixed points in compactifications and combinatorial counterparts ⋮ All those Ramsey classes (Ramsey classes with closures and forbidden homomorphisms) ⋮ Unnamed Item ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Topics in topology
• Metric spaces are Ramsey
• Canonical partitions of universal structures
• On the geometry of Urysohn's universal metric space
• The isometry group of the Urysohn space as a Lévy group
• The oscillation stability problem for the Urysohn sphere: a combinatorial approach
• Globalization of the partial isometries of metric spaces and local approximation of the group of isometries of Urysohn space
• An oscillation theorem for groups of isometries
• Ramsey degrees of finite ultrametric spaces, ultrametric Urysohn spaces and dynamics of their isometry groups
• Ramsey classes of set systems
• Any separable ultrametric space can be isometrically imbedded in \(l_ 2\)
• A Ramsey theorem for trees
• Lipschitz functions on classical spaces
• Extending partial isomorphisms of graphs
• Partitions of finite relational and set systems
• Symmetries and Ramsey properties of trees
• On the divisibility of homogeneous hypergraphs
• The distortion problem
• Recent trends in Euclidean Ramsey theory
• On Ramsey sets in spheres
• Euclidean Ramsey theorems. I
• A course in model theory. An introduction to contemporary mathematical logic. Transl. from the French by Moses Klein
• Theory of relations. Transl. from the French by P. Clote. With an appendix by Norbert Sauer.
• Ramsey-Milman phenomenon, Urysohn metric spaces, and extremely amenable groups
• A Ramsey theorem for countable homogeneous directed graphs
• Indivisible homogeneous directed graphs and a game for vertex partitions
• The indivisibility of the homogeneous \(K_ n\)-free graphs
• Minimal actions of the group \(\mathbb{S}(\mathbb{Z})\) of permutations of the integers
• The Urysohn universal metric space is homeomorphic to a Hilbert space
• Isometric embedding of finite ultrametric spaces in Banach spaces
• Ubiquity in category for metric spaces and transition systems
• The classification of metrics and multivariate statistical analysis
• Divisibility of countable metric spaces
• Extending partial isometries
• Some isometry groups of the Urysohn space
• Six theorems about injective metric spaces
• Ramsey's theorem for a class of categories
• Fraïssé limits, Ramsey theory, and topological dynamics of automorphism groups
• Extension and reconstruction theorems for the Urysohn universal metric space
• Stabilizers of closed sets in the Urysohn space
• Computing the complexity of the relation of isometry between separable Banach spaces
• A Partition Property of Simplices in Euclidean Space
• Big Ramsey Degrees and Divisibility in Classes of Ultrametric Spaces
• Introduction to Ramsey Spaces (AM-174)
• A Topological Application of the Isoperimetric Inequality
• Espaces ultramétriques
• Regularity and Positional Games
• On free actions, minimal flows, and a problem by Ellis
• A theorem on isotropic spaces
• Metrically homogeneous spaces
• A note on the Banach-Mazur problem
• Canonical Vertex Partitions
• Ramsey Classes and Homogeneous Structures
• On the classification of Polish metric spaces up to isometry
• Lipschitz-free Banach spaces
• Random metric spaces and universality
• On the universal ultrametric space
• Ramsey's Theorem for n-Parameter Sets
• Asymmetric graphs
• Sur l'extension aux relations de quelques propriétés des ordres
• Sur un espace métrique séparable universel

This page was built for publication: Structural Ramsey theory of metric spaces and topological dynamics of isometry groups