Fra\"iss\'e structures and a conjecture of Furstenberg

Dana Bartošová; Andy Zucker

Fra\"iss\'e structures and a conjecture of Furstenberg

Dynamical Systems 2018-09-11 v2 Group Theory Logic

Authors: Dana Bartošová , Andy Zucker

Abstract

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 ultrafilter on a countable set.

Keywords

ultrafilter topological semigroups topological groups

Cite

@article{arxiv.1802.02513,
  title  = {Fra\"iss\'e structures and a conjecture of Furstenberg},
  author = {Dana Bartošová and Andy Zucker},
  journal= {arXiv preprint arXiv:1802.02513},
  year   = {2018}
}

Comments

Formerly titled "Samuel compactifications of automorphism groups," the paper was accepted in Comment. Math. Univ. Carolin., and the title was changed at the request of the referee

Fra\"iss\'e structures and a conjecture of Furstenberg

Abstract

Keywords

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