Geodesic
Fraïssé structures and a conjecture of Furstenberg
Commentationes Mathematicae Universitatis Carolinae, Tome 60 (2019) no. 1, pp. 1-24.

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We study problems concerning the Samuel compactification of the automorphism group of a countable first-order structure. A key motivating question is a problem of Furstenberg and a counter-conjecture by Pestov regarding the difference between $S(G)$, the Samuel compactification, and $E(M(G))$, the enveloping semigroup of the universal minimal flow. We resolve Furstenberg's problem for several automorphism groups and give a detailed study in the case of $G= S_\infty$, leading us to define and investigate several new types of ultrafilters on a countable set.
DOI : 10.14712/1213-7243.2015.276
Classification : 03E05, 05C63, 22F50, 37B05
Keywords: Fraïssé structures; enveloping semigroups; universal minimal flow 
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Bartošová, Dana; Zucker, Andy. Fraïssé structures and a conjecture of Furstenberg. Commentationes Mathematicae Universitatis Carolinae, Tome 60 (2019) no. 1, pp. 1-24. doi : 10.14712/1213-7243.2015.276. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.276/

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