18 citations · 56 across the 19 of their papers we have counts for
25 papers
Topological groups with tractable minimal dynamics
Gianluca Basso, Andy Zucker
A Polish group has the generic point property if any minimal -flow admits a comeager orbit, or equivalently if the universal minimal flow (UMF) does. The class $\mathsf{GPP}…
Ultracoproducts and weak containment for flows of topological groups
Andy Zucker
We develop the theory of ultracoproducts and weak containment for flows of arbitrary topological groups. This provides a nice complement to corresponding theories for p.m.p. action…
Type-respecting amalgamation and big Ramsey degrees
Andrés Aranda, Samuel Braunfeld, David Chodounský +4
We give an infinitary extension of the Nešetřil-Rödl theorem for category of relational structures with special type-respecting embeddings.
Characterisation of the big Ramsey degrees of the generic partial order
Martin Balko, David Chodounský, Natasha Dobrinen +4
As a result of 33 intercontinental Zoom calls, we characterise big Ramsey degrees of the generic partial order. This is an infinitary extension of the well known fact that finite p…
Infinite-dimensional Ramsey theory for binary free amalgamation classes
Natasha Dobrinen, Andy Zucker
We develop infinite-dimensional Ramsey theory for Fraïssé limits of finitely constrained free amalgamation classes in finite binary languages. We show that our approach is optimal…
Polish space partition principles and the Halpern-Läuchli theorem
Chris Lambie-Hanson, Andy Zucker
The Halpern-Läuchli theorem, a combinatorial result about trees, admits an elegant proof due to Harrington using ideas from forcing. In an attempt to distill the combinatorial esse…
From Ramsey degrees to Ramsey expansions via weak amalgamation
Dragan Mašulović, Andy Zucker
Under no additional assumptions, in this paper we construct a Ramsey expansion for every category of finite objects with finite small Ramsey degrees. Our construction is based on t…
Minimal subdynamics and minimal flows without characteristic measures
Joshua Frisch, Brandon Seward, Andy Zucker
Given a countable group and a -flow , a measure is called characteristic if it is -invariant. Frisch and Tamuz asked about the existence o…
Exact big Ramsey degrees for finitely constrained binary free amalgamation classes
Martin Balko, David Chodounský, Natasha Dobrinen +4
We characterize the big Ramsey degrees of free amalgamation classes in finite binary languages defined by finitely many forbidden irreducible substructures, thus refining the recen…
Topological dynamics beyond Polish groups
Gianluca Basso, Andy Zucker
When is a Polish group, metrizability of the universal minimal flow has been shown to be a robust dividing line in the complexity of the topological dynamics of . We introdu…
Minimal model-universal flows for locally compact Polish groups
Colin Jahel, Andy Zucker
Let be a locally compact Polish group. A metrizable -flow is called model-universal if by considering the various invariant probability measures on , we can recover e…
On big Ramsey degrees for binary free amalgamation classes
Andy Zucker
Generalizing and simplifying recent work of Dobrinen, we show that if is a finite binary relational language and is a finite set of finite irreducible $…
Universal minimal flows of homeomorphism groups of high-dimensional manifolds are not metrizable
Yonatan Gutman, Todor Tsankov, Andy Zucker
Answering a question of Uspenskij, we prove that if is a closed manifold of dimension or higher or the Hilbert cube, then the universal minimal flow of …
Minimal flows with arbitrary centralizer
Andy Zucker
Given any pair of countable groups and with infinite, we construct a minimal, free, Cantor -flow so that embeds into the group of automorphisms of .
A note on minimal models for pmp actions
Andy Zucker
Given a countable group , we say that a metrizable flow is model-universal if by considering the various invariant measures on , we can recover every free measure-preserv…
Topological dynamics of Polish group extensions
Colin Jahel, Andy Zucker
We consider a short exact sequence of Polish groups and consider what can be deduced about the dynamics of given information about the dynamics of a…
Bernoulli disjointness
Eli Glasner, Todor Tsankov, Benjamin Weiss +1
Generalizing a result of Furstenberg, we show that for every infinite discrete group , the Bernoulli flow is disjoint from every minimal -flow. From this, we deduce tha…
Maximally highly proximal flows
Andy Zucker
For a Polish group, we consider -flows which either contain a comeager orbit or have all orbits meager. We single out a class of flows, the maximally highly proximal (MHP) f…
Bernoulli disjointness and maximally almost periodic groups
Andy Zucker
We show that any discrete group containing an infinite, normal, maximally almost periodic subgroup has the Bernoulli Disjointness Property, or BDJ. Also, any group containing enoug…
Fraïssé structures and a conjecture of Furstenberg
Dana Bartošová, Andy Zucker
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…
A direct solution to the Generic Point Problem
Andy Zucker
We provide a new proof of a recent theorem of Ben-Yaacov, Melleray, and Tsankov. If is a Polish group and is a minimal, metrizable -flow with all orbits meager, then the…
Big Ramsey degrees and topological dynamics
Andy Zucker
We consider Fraïssé structures whose objects have finite big Ramsey degree and ask what consequences this has for the dynamics of the automorphism group. Motivated by a theorem of…
Thick, syndetic, and piecewise syndetic subsets of Fraïssé structures
Andy Zucker
We define and undertake a systematic study of thick, syndetic, and piecewise syndetic subsets of a Fraïssé structure. Each of these collections forms a family in the sense of Akin…
Topological Dynamics of Closed Subgroups of
Andy Zucker
For a closed subgroup of , we provide an explicit characterization of the greatest -ambit. Using this, we provide a precise characterization of when has metr…