Maciej Malicki
Maciej Malicki: Infinitary continuous logic and descriptive set theory
03/06/21 09:27
Tuesday, June 8, 2021 17:00
Location: Zoom.us: if you want to participate please contact organizers
Speaker: Maciej Malicki (Polish Academy of Sciences)
Title: Infinitary continuous logic and descriptive set theory
Abstract: There are deep connections between model theory of the infinitary logic and descriptive set theory: Scott analysis, the López-Escobar theorem or the Suzuki theorem are well known examples of this phenomenon. In this talk, I will present results of a research devoted to generalizing these connections to the setting of continuous infinitary logic and Polish metric structures. In particular, I will discuss a continuous counterpart of a theorem of Hjorth and Kechris characterizing essential countability of the isomorphism relation on a given Borel class of countable structures. As an application, I will give a short model-theoretic proof of a result of Kechris saying that orbit equivalence relations induced by continuous actions of locally compact Polish groups are essentially countable. This is joint work with Andreas Hallbäck and Todor Tsankov.
Location: Zoom.us: if you want to participate please contact organizers
Speaker: Maciej Malicki (Polish Academy of Sciences)
Title: Infinitary continuous logic and descriptive set theory
Abstract: There are deep connections between model theory of the infinitary logic and descriptive set theory: Scott analysis, the López-Escobar theorem or the Suzuki theorem are well known examples of this phenomenon. In this talk, I will present results of a research devoted to generalizing these connections to the setting of continuous infinitary logic and Polish metric structures. In particular, I will discuss a continuous counterpart of a theorem of Hjorth and Kechris characterizing essential countability of the isomorphism relation on a given Borel class of countable structures. As an application, I will give a short model-theoretic proof of a result of Kechris saying that orbit equivalence relations induced by continuous actions of locally compact Polish groups are essentially countable. This is joint work with Andreas Hallbäck and Todor Tsankov.
Maciej Malicki: Groups of isometries of Polish ultrametric spaces
10/11/14 15:07
Tuesday, November 18, 2014 17:15
Room: D1-215
Speaker: Maciej Malicki
Title: Groups of isometries of Polish ultrametric spaces
Abstract. We will characterize Polish ultrametric spaces whose isometry groups have a neighborhood basis at the identity consisting of open subgroups with ample generics. We will also define Polish ultrametric W-spaces and give a characterization of W-spaces whose isometry groups have uncountable strong cofinality.
Room: D1-215
Speaker: Maciej Malicki
Title: Groups of isometries of Polish ultrametric spaces
Abstract. We will characterize Polish ultrametric spaces whose isometry groups have a neighborhood basis at the identity consisting of open subgroups with ample generics. We will also define Polish ultrametric W-spaces and give a characterization of W-spaces whose isometry groups have uncountable strong cofinality.