A combinatorial proof of the extension property for partial isometries

DOI10.14712/1213-7243.2015.275OpenAlexW2963377404WikidataQ127533769 ScholiaQ127533769MaRDI QIDQ5227145

Jaroslav Nešetřil, Matěj Konečný, Jan Hubička

Publication date: 5 August 2019

Published in: Commentationes Mathematicae Universitatis Carolinae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.10976

zbMATH Keywords

metric spaceamalgamation classhomogeneous structureextension property for partial automorphismsHrushovski property

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Metric spaces, metrizability (54E35) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05) Infinite automorphism groups (20B27) Groups as automorphisms of other structures (22F50) Group actions on combinatorial structures (05E18)

Related Items (6)

All those EPPA classes (strengthenings of the Herwig–Lascar theorem) ⋮ ON EXTENSIONS OF PARTIAL ISOMORPHISMS ⋮ Dense locally finite subgroups of automorphism groups of ultraextensive spaces ⋮ Extending partial isometries of antipodal graphs ⋮ The Hrushovski property for hypertournaments and profinite topologies ⋮ EPPA for two-graphs and antipodal metric spaces

Cites Work

• Metric spaces are Ramsey
• A theorem of Hrushovski-Solecki-Vershik applied to uniform and coarse embeddings of the Urysohn metric space
• Globalization of the partial isometries of metric spaces and local approximation of the group of isometries of Urysohn space
• Ramsey theorem for designs
• All those Ramsey classes (Ramsey classes with closures and forbidden homomorphisms)
• Extending partial isometries
• Ergodic theory and virtual groups
• Finitely approximate groups and actions Part I: The Ribes–Zalesskiĭ property
• A structural generalization of the Ramsey theorem
• On The Profinite Topology on a Free Group
• AUTOMATIC CONTINUITY FOR ISOMETRY GROUPS
• Finite Conformal Hypergraph Covers and Gaifman Cliques in Finite Structures
• Extending partial automorphisms and the profinite topology on free groups
• All those EPPA classes (strengthenings of the Herwig–Lascar theorem)
• COHERENT EXTENSION OF PARTIAL AUTOMORPHISMS, FREE AMALGAMATION AND AUTOMORPHISM GROUPS
• Conant's generalised metric spaces are Ramsey
• The Hrushovski property for hypertournaments and profinite topologies
• EPPA for two-graphs and antipodal metric spaces
• Coset Representations in Free Groups

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