Approximate isomorphism of randomization pairs

Autor: James Hanson, Tomás Ibarlucía

We study approximate $\aleph_0$-categoricity of theories of beautiful pairs of randomizations, in the sense of continuous logic. This leads us to disprove a conjecture of Ben Yaacov, Berenstein and Henson, by exhibiting $\aleph_0$-categorical, $\alep

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::12b479cb9498ab4eda1b4796c53870e9

Dynamical simplices and minimal homeomorphisms

Autor: Tomás Ibarlucía, Julien Melleray

Publikováno v: Proceedings of the American Mathematical Society. 145:4981-4994

We give a characterization of sets K K of probability measures on a Cantor space X X with the property that there exists a minimal homeomorphism g g of X X such that the set of g g -invariant probability measures on X X coincides with K K . This exte

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::de5ecd62f198b7271758c503eb6529cd
https://doi.org/10.1090/proc/13578

Maximal equivariant compactification of the Urysohn spaces and other metric structures

Autor: Tomás Ibarlucía, Michael Megrelishvili

Publikováno v: Advances in Mathematics. 380:107599

We study isometric $G$-spaces and the question of when their maximal equivariant compactification is the Gromov compactification (meaning that it coincides with the compactification generated by the distance functions to points). Answering questions

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::794a8c3ffc9403fa05f428cb4ffcacfe
https://doi.org/10.1016/j.aim.2021.107599

Full groups of minimal homeomorphisms and Baire category methods

Autor: Julien Melleray, Tomás Ibarlucía

Publikováno v: Ergodic Theory and Dynamical Systems
Ergodic Theory and Dynamical Systems, Cambridge University Press (CUP), 2016, 36 (2), pp.550--573

We study full groups of minimal actions of countable groups by homeomorphisms on a Cantor space$X$, showing that these groups do not admit a compatible Polish group topology and, in the case of$\mathbb{Z}$-actions, are coanalytic non-Borel inside$\te

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https://doi.org/10.1017/etds.2014.75

Automorphism groups of randomized structures

Autor: Tomás Ibarlucía

We study automorphism groups of randomizations of separable structures, with focus on the $\aleph_0$-categorical case. We give a description of the automorphism group of the Borel randomization in terms of the group of the original structure. In the

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0ee84b57e57cdb594fa00a2effc8aab0