Seminarium:
Teoria modeli
Osoba referująca:
Krzysztof Krupiński (University of Wrocław)
Data:
środa, 26. Luty 2020 - 16:15
Sala:
602
Opis:
The general motivation standing behind this research is to understand
relationships between dynamical and model-theoretic properties of
definable [topological] groups and between dynamical properties of groups
of automorphisms of first order structures and model-theoretic properties
of the underlying theories. More specifically, our goal is to understand
model-theoretic consequences of various notions of amenability.
Among the notions of amenability that we are interested in are: definable amenability of a definable group, classical amenability of a topological group, and, more generally, [weak] definable topological amenability of a definable topological group. We also introduce and study amenable theories.
The consequences of amenability that we obtain are the appropriate versions of G-compactness: for first order theories this is the equality of Lascar strong types and Kim-Pillay strong types; for definable [topological] groups this is the equality of suitably defined connected components $G^{000}$ and $G^{00}$ of the group $G$ in question.
Among our main technical tools, of interest in its own right, is an elaboration on and strengthening of the Massicot-Wagner version of the stabilizer theorem, and also some results about measures and measure-like functions.
My series of talks will be based on my preprint “Amenability and definability” joint with Ehud Hrushovski and Anand Pillay. In the first series of talks, I will focus on the context of definable [topological] groups; the second series will be devoted to our new notion of amenable theory.
Among the notions of amenability that we are interested in are: definable amenability of a definable group, classical amenability of a topological group, and, more generally, [weak] definable topological amenability of a definable topological group. We also introduce and study amenable theories.
The consequences of amenability that we obtain are the appropriate versions of G-compactness: for first order theories this is the equality of Lascar strong types and Kim-Pillay strong types; for definable [topological] groups this is the equality of suitably defined connected components $G^{000}$ and $G^{00}$ of the group $G$ in question.
Among our main technical tools, of interest in its own right, is an elaboration on and strengthening of the Massicot-Wagner version of the stabilizer theorem, and also some results about measures and measure-like functions.
My series of talks will be based on my preprint “Amenability and definability” joint with Ehud Hrushovski and Anand Pillay. In the first series of talks, I will focus on the context of definable [topological] groups; the second series will be devoted to our new notion of amenable theory.