Fraïssé structures and a conjecture of Furstenberg

@article{Bartovsova2019FrassSA,
  title={Fra{\"i}ss{\'e} structures and a conjecture of Furstenberg},
  author={Dana Bartovsov'a and Andy Zucker},
  journal={Commentationes Mathematicae Universitatis Carolinae},
  year={2019}
}
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

References

SHOWING 1-10 OF 20 REFERENCES
Polish groups with metrizable universal minimal flows
We prove that if the universal minimal flow of a Polish group $G$ is metrizable and contains a $G_\delta$ orbit $G \cdot x_0$, then it is isomorphic to the completion of the homogeneous spaceExpand
Metrizable universal minimal flows of Polish groups have a comeagre orbit
We prove that, whenever G is a Polish group with metrizable universal minimal flow M(G), there exists a comeagre orbit in M(G). It then follows that there exists an extremely amenable, closed,Expand
Some universal constructions in abstract topological dynamics
This small survey of basic universal constructions related to the actions of topological groups on compacta is centred around a new result --- an intrinsic description of extremely amenableExpand
ON FREE ACTIONS, MINIMAL FLOWS, AND A PROBLEM BY ELLIS
We exhibit natural classes of Polish topological groups G such that every continuous action of G on a compact space has a fixed point, and observe that every group with this property provides aExpand
Forcing with Filters and Complete Combinatorics
  • C. Laflamme
  • Mathematics, Computer Science
  • Ann. Pure Appl. Log.
  • 1989
TLDR
It is shown that in most cases the combinatorics satisfied by the ultrafilters recapture the forcing notion in the Levy model. Expand
Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation
  • H. Furstenberg
  • Mathematics, Computer Science
  • Mathematical systems theory
  • 2005
TLDR
The objects of ergodic theory -measure spaces with measure-preserving transformation groups- will be called processes, those of topological dynamics-compact metric spaces with groups of homeomorphisms-will be called flows, and what may be termed the "arithmetic" of these classes of objects is concerned. Expand
Ultrafilters on a countable set
An ultrafilter on a set is a proper collection of subsets of ' that set which is maximal among such collections having the finite intersection property. Ultrafilters were popularized by N.BourbakiExpand
Minimal actions of the group $ {\Bbb S(Z)} $ of permutations of the integers
Abstract. Each topological group G admits a unique universal minimal dynamical system (M(G),G). For a locally compact non-compact group this is a nonmetrizable system with a very rich structure, onExpand
Interpolation sets for subalgebras ofl∞(Z)
LetU be the subalgegra ofl∞(Z) generated by the minimal functions. The collection ofU-interpolation sets is identified as the ideal of small subsets ofZ. General theorems about the relation betweenExpand
Algebra in the Stone-Čech Compactification by Neil Hindman and Dona Strauss
This is an excellent book. This review is an attempt to convince the reader that this verdict is not the prejudice of an enthusiast but a sober, sound judgement. The title might suggest that theExpand
...
1
2
...