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Preprint Number 1417
1417. Krzysztof Krupiński, Tomasz Rzepecki Galois groups as quotients of Polish groups E-mail: Submission date: 24 April 2018 Abstract: We present the (Lascar) Galois group of any countable theory as a
quotient of
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
Pillay,
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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