8 papers
Relative Property (T), simplices of invariant measures, and existentially closed models
Tomás Ibarlucía
We prove a Bauer-Poulsen dichotomy theorem for simplices of invariant measures associated with permutation groups. More precisely, let be a transitive group of permutations of…
Existentially closed measure-preserving actions of free groups
Alexander Berenstein, C. Ward Henson, Tomás Ibarlucía
This paper is motivated by the study of probability measure-preserving (pmp) actions of free groups using continuous model theory. Such an action is treated as a metric structure t…
Approximate isomorphism of randomization pairs
James Hanson, Tomás Ibarlucía
We study approximate -categoricity of theories of beautiful pairs of randomizations, in the sense of continuous logic. This leads us to disprove a conjecture of Ben Yaaco…
Maximal equivariant compactification of the Urysohn spaces and other metric structures
Tomás Ibarlucía, Michael Megrelishvili
We study isometric -spaces and the question of when their maximal equivariant compactification is the Gromov compactification (meaning that it coincides with the compactificatio…
Infinite-dimensional Polish groups and Property (T)
Tomás Ibarlucía
We show that all groups of a distinguished class of «large» topological groups, that of Roelcke precompact Polish groups, have Kazhdan's Property (T). This answers a question of Ts…
A model-theoretic approach to rigidity of strongly ergodic, distal actions
Tomás Ibarlucía, Todor Tsankov
We develop a model-theoretic framework for the study of distal factors of strongly ergodic, measure-preserving dynamical systems of countable groups. Our main result is that all su…
Eberlein oligomorphic groups
Itaï Ben Yaacov, Tomás Ibarlucía, Todor Tsankov
We study the Fourier--Stieltjes algebra of Roelcke precompact, non-archimedean, Polish groups and give a model-theoretic description of the Hilbert compactification of these groups…
Dynamical simplices and minimal homeomorphisms
Tomás Ibarlucía, Julien Melleray
We give a characterization of sets K of probability measures on a Cantor space X with the property that there exists a minimal homeomorphism g of X such that the set of g-invariant…