In this thesis, we present a new viewpoint of the universal minimal flow in the language of near ultrafilters. We apply this viewpoint to generalize results of Kechris, Pestov and Todorcevic about a connection between groups of automorphisms of structures and structural Ramsey theory from countable to uncountable structures. This allows us to provide new examples of explicit descriptions of universal minimal flows as well as of extremely amenable groups.
We identify new classes of finite structures satisfying the Ramsey property and apply the result to the computation of the universal minimal flow of the group of automorphisms of $\P(\omega_1)/\fin$ as well as of certain closed subgroups of groups of homeomorphisms of Cantor cubes. We furthermore apply our theory to groups of isometries of metric spaces and the problem of unique amenability of topological groups.
The theory combines tools from set theory, model theory, Ramsey theory, topological dynamics and ergodic theory, and homogeneous structures.
| Identifer | oai:union.ndltd.org:TORONTO/oai:tspace.library.utoronto.ca:1807/43472 |
| Date | 07 January 2014 |
| Creators | Bartosova, Dana |
| Contributors | Todorcevic, Stevo |
| Source Sets | University of Toronto |
| Language | en_ca |
| Detected Language | English |
| Type | Thesis |
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