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Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures

Published online by Cambridge University Press:  20 November 2018

Dana Bartošová
Dana Bartošová*
Affiliation:
Department of Mathematics, University of Toronto, Bahen Center, 40 St. George St., Toronto, ON M5S 2E4 e-mail: dana.bartosova@utoronto.ca Faculty of Mathematics and Physics, Charles University in Prague, Ke Karlovu 3, 121 16 Prague, Czech Republic M5S 2E4
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Abstract.

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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 Fraϊssé theory and Ramsey theory. This work generalizes some of the known results about countable structures

Keywords

37B0503E0205D1022F5054H20universal minimal flowsultrafilter flowsRamsey theory
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 4 , 01 December 2013 , pp. 709 - 722
Copyright
Copyright © Canadian Mathematical Society 2013

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