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Preprint Number 935
935. Krzysztof Krupiński, Anand Pillay and Tomasz Rzepecki
Topological dynamics and the complexity of strong types
Submission date: 1st October 2015.
We develop topological dynamics for the group of automorphisms of a monster
model of any given theory. In particular, we find strong relationships between
objects from topological dynamics (such as the generalized Bohr
compactification introduced by Glasner) and various Galois groups of the theory
in question, obtaining essentially new information about them, e.g. we present
the closure of the identity in the Lascar Galois group of the theory as the
quotient of a compact, Hausdorff group by a dense subgroup.
Let C be a monster model of a countable theory, p in
S(∅), and E be a bounded, Borel (or even analytic) equivalence
relation on p(C). Then, exactly one of the following holds:
All the results which we obtain for bounded, invariant equivalence relations carry over to the case of bounded index, invariant subgroups of definable groups.
Mathematics Subject Classification: 03C45, 54H20, 03E15, 54H11
Keywords and phrases:
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