Universal flows of closed subgroups of $S_{\infty}$ and relative extreme amenability

Details Universal flows of closed subgroups of $S_{\infty}$ and relative extreme amenability Universal flows of closed subgroups of $S_{\infty}$ and relative extreme amenability

2012-01-06

arxiv.org/abs/1201.1472v2

Mathematics

Logic

13 pages. Some typos corrected

Scientific paper

This paper is devoted to the study of universality for a particular continuous action naturally attached to certain pairs of closed subgroups of $S_{\infty}$. It shows that three new concepts, respectively called relative extreme amenability, relative Ramsey property for embeddings, and relative Ramsey property for structures, are relevant in order to understand this property correctly. It also allows to provide a partial answer to a question posed by Kechris, Pestov and Todorcevic.

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