Fraïssé structures and a conjecture of Furstenberg

Dana Bartošová; Andy Zucker

Commentationes Mathematicae Universitatis Carolinae (2019)

  • Volume: 60, Issue: 1, page 1-24
  • ISSN: 0010-2628

Abstract

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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 ∞ , leading us to define and investigate several new types of ultrafilters on a countable set.

How to cite

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Bartošová, Dana, and Zucker, Andy. "Fraïssé structures and a conjecture of Furstenberg." Commentationes Mathematicae Universitatis Carolinae 60.1 (2019): 1-24. <http://eudml.org/doc/294231>.

@article{Bartošová2019,
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 ultrafilters on a countable set.},
author = {Bartošová, Dana, Zucker, Andy},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Fraïssé structures; enveloping semigroups; universal minimal flow},
language = {eng},
number = {1},
pages = {1-24},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Fraïssé structures and a conjecture of Furstenberg},
url = {http://eudml.org/doc/294231},
volume = {60},
year = {2019},
}

TY - JOUR
AU - Bartošová, Dana
AU - Zucker, Andy
TI - Fraïssé structures and a conjecture of Furstenberg
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2019
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 60
IS - 1
SP - 1
EP - 24
AB - 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.
LA - eng
KW - Fraïssé structures; enveloping semigroups; universal minimal flow
UR - http://eudml.org/doc/294231
ER -

References

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