Fraïssé structures and a conjecture of Furstenberg

  title={Fra{\"i}ss{\'e} structures and a conjecture of Furstenberg},
  author={Dana Bartovsov'a and Andy Zucker},
  journal={Commentationes Mathematicae Universitatis Carolinae},
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… Expand


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