Universal Flows of Closed Subgroups of S∞ and Relative Extreme Amenability

Abstract

This paper is devoted to the study of universality for a particular continuous action naturally attached to certain pairs of closed subgroups of S ∞. 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 us to provide a partial answer to a question posed in [2] by Kechris, Pestov and Todorcevic (Geom. Funct. Anal. 15(1), 106-189, 2005). © Springer Science+Business Media New York 2013.