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SMOOTHNESS OF BOUNDED INVARIANT EQUIVALENCE RELATIONS

  • KRZYSZTOF KRUPIŃSKI (a1) and TOMASZ RZEPECKI (a2)
Abstract

We generalise the main theorems from the paper “The Borel cardinality of Lascar strong types” by I. Kaplan, B. Miller and P. Simon to a wider class of bounded invariant equivalence relations. We apply them to describe relationships between fundamental properties of bounded invariant equivalence relations (such as smoothness or type-definability) which also requires finding a series of counterexamples. Finally, we apply the generalisation mentioned above to prove a conjecture from a paper by the first author and J. Gismatullin, showing that the key technical assumption of the main theorem (concerning connected components in definable group extensions) from that paper is not only sufficient but also necessary to obtain the conclusion.

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[3]Gismatullin, Jakub and Krupiński, Krzysztof, On model-theoretic connected components in some group extensions, Version 2, 2013, arXiv: 1201.5221v2, submitted.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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