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Preprint Number 1417
1417. Krzysztof Krupiński, Tomasz Rzepecki
Galois groups as quotients of Polish groups
Submission date: 24 April 2018
We present the (Lascar) Galois group of any countable theory as a
a compact Polish group by an F_σ normal subgroup: in general, as a
topological group, and under NIP, also in terms of Borel cardinality. This
allows us to obtain similar results for arbitrary strong types defined on a
single complete type over ∅. As an easy conclusion of our main
theorem, we get the main result from our recent paper joint with Anand
which says that for any strong type defined on a single complete type over
∅, smoothness is equivalent to type-definability.
Mathematics Subject Classification: 03C45, 54H20, 22C05, 03E15, 54H11
Keywords and phrases: topological dynamics, Galois groups, Polish groups, strong types,Borel cardinality, Rosenthal compacta.
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