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# Article

 Title: Fraïssé structures and a conjecture of Furstenberg (English) Author: Bartošová, Dana Author: Zucker, Andy Language: English Journal: Commentationes Mathematicae Universitatis Carolinae ISSN: 0010-2628 (print) ISSN: 1213-7243 (online) Volume: 60 Issue: 1 Year: 2019 Pages: 1-24 Summary lang: English . Category: math . Summary: 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. (English) Keyword: Fraïssé structures Keyword: enveloping semigroups Keyword: universal minimal flow MSC: 03E05 MSC: 05C63 MSC: 22F50 MSC: 37B05 idZBL: Zbl 07088822 idMR: MR3946661 DOI: 10.14712/1213-7243.2015.276 . Date available: 2019-05-13T07:43:12Z Last updated: 2021-04-05 Stable URL: http://hdl.handle.net/10338.dmlcz/147667 . Reference: [1] Ajtai M., Komlós J., Szemerédi E.: A note on Ramsey numbers.J. Combin. Theory Ser. A 29 (1980), no. 3, 354–360. MR 0600598, 10.1016/0097-3165(80)90030-8 Reference: [2] Auslander J.: Minimal Flows and Their Extensions.North-Holland Mathematics Studies, 153, Mathematical Notes, 122, North-Holland Publishing, Amsterdam, 1988. 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