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# Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures

Published:2012-07-27
Printed: Dec 2013
• Dana Bartošová,
Department of Mathematics, University of Toronto, Bahen Center, 40 St. George St., Toronto, ON M5S 2E4
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## Abstract

It is a well-known fact, that the greatest ambit for a topological group $G$ is the Samuel compactification of $G$ with respect to the right uniformity on $G.$ We apply the original description by Samuel from 1948 to give a simple computation of the universal minimal flow for groups of automorphisms of uncountable structures using Fraïssé theory and Ramsey theory. This work generalizes some of the known results about countable structures.
 Keywords: universal minimal flows, ultrafilter flows, Ramsey theory
 MSC Classifications: 37B05 - Transformations and group actions with special properties (minimality, distality, proximality, etc.) 03E02 - Partition relations 05D10 - Ramsey theory [See also 05C55] 22F50 - Groups as automorphisms of other structures 54H20 - Topological dynamics [See also 28Dxx, 37Bxx]