CONSEQUENCES OF THE EXISTENCE OF AMPLE GENERICS AND AUTOMORPHISM GROUPS OF HOMOGENEOUS METRIC STRUCTURES

DOI10.1017/jsl.2015.73zbMath1403.03087arXiv1405.1532OpenAlexW2963261474MaRDI QIDQ2976368

Maciej Malicki

Publication date: 28 April 2017

Published in: The Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1405.1532

zbMATH Keywords

automatic continuitysmall index propertyPolish groupsmetric structuresuncountable cofinality

Mathematics Subject Classification ID

Descriptive set theory (03E15) Topological groups (topological aspects) (54H11) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05)

Related Items (3)

AUTOMATIC CONTINUITY FOR ISOMETRY GROUPS ⋮ Isometry groups of Borel randomizations ⋮ Polish topologies on groups of non-singular transformations

Cites Work

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• Automatic continuity of homomorphisms and fixed points on metric compacta
• Extending partial isomorphisms of graphs
• Generic automorphisms and graph coloring
• Generic elements in isometry groups of Polish ultrametric spaces
• Extending partial isometries
• Automatic continuity for the unitary group
• Polish topometric groups
• The automorphism group of the Lebesgue measure has no non-trivial subgroups of index <2^ω
• The Small Index Property for Free Groups and Relatively Free Groups
• Turbulence, amalgamation, and generic automorphisms of homogeneous structures
• Topological groups with Rokhlin properties

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