2018
DOI: 10.1007/s11856-018-1780-3
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Topological dynamics and the complexity of strong types

Abstract: 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.We… Show more

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Cited by 19 publications
(56 citation statements)
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“…Some deep results in this direction were obtained in [KMS14; KM14;KR16]. A completely new approach via topological dynamics was developed in [KP17b;KPR15]. In particular, in [KPR15], it was proved that the descriptive set theoretic smoothness of a strong type defined on a single complete type over ∅ is equivalent to its type-definability.…”
Section: Introductionmentioning
confidence: 99%
See 4 more Smart Citations
“…Some deep results in this direction were obtained in [KMS14; KM14;KR16]. A completely new approach via topological dynamics was developed in [KP17b;KPR15]. In particular, in [KPR15], it was proved that the descriptive set theoretic smoothness of a strong type defined on a single complete type over ∅ is equivalent to its type-definability.…”
Section: Introductionmentioning
confidence: 99%
“…A completely new approach via topological dynamics was developed in [KP17b;KPR15]. In particular, in [KPR15], it was proved that the descriptive set theoretic smoothness of a strong type defined on a single complete type over ∅ is equivalent to its type-definability. The key idea was to present the Galois group as a quotient of a compact Hausdorff group, which is interesting in its own right.…”
Section: Introductionmentioning
confidence: 99%
See 3 more Smart Citations