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Bounded Invariant Equivalence Relations
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We study strong types and Galois groups in model theory from a topological and descriptive-set-theoretical point of view, leaning heavily on topological dynamical tools. More precisely, we give an abstract (not model theoretic) treatment of problems related to cardinality and Borel cardinality of strong types, quotients of definable groups and related objecets, generalising (and often improving) essentially all hitherto known results in this area. In particular, we show that under reasonable assumptions, strong type spaces are "locally" quotients of compact Polish groups. It follows that they are smooth if and only if they are type-definable, and that a quotient of a type-definable group by an analytic subgroup is either finite or of cardinality at least continuum.
Forward citations
Cited by 2 Pith papers
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Some results on NIP groups and their Ellis groups
In NIP theories, the Ellis group of any definable group has size at most 2^|T|, independent of the model; under bounded VC-codensity it (and the local quotient G/G^00_φ) is an inverse limit of compact Lie groups of di...
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Convolution semigroups for automorphism dynamics
A new convolution operation on invariant Keisler measures over arbitrary theories, transferred from Ellis semigroups of automorphism flows, classifies idempotents by relatively type-definable subgroups of Aut(C).
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