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Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures |
13 pages
Published:2012-07-27
- Dana Bartošová,
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] |