Polish groups with metrizable universal minimal flows

Julien Melleray (1) , Lionel Nguyen van Thé (2) , Todor Tsankov (3)

1 AGL - Algèbre, géométrie, logique
2 I2M - Institut de Mathématiques de Marseille
3 IMJ - Institut de Mathématiques de Jussieu

We prove that if the universalminimal flow of a Polish group G is metrizable and contains a comeagre orbit O, then it is isomorphic to the completion of the homogeneous space G/O and show how this result translates naturally in terms of structural Ramsey theory. We also investigate universal minimal proximal flows and describe concrete representations of them in a number of examples.

Domains: Logic [math.LO]

Julien Melleray, Lionel Nguyen van Thé, Todor Tsankov. Polish groups with metrizable universal minimal flows. International Mathematics Research Notices, 2015, 2016 (5), pp.1285-1307. ⟨10.1093/imrn/rnv171⟩. ⟨hal-00983248⟩