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SMOOTHNESS OF BOUNDED INVARIANT EQUIVALENCE RELATIONS

Published online by Cambridge University Press:  09 March 2016

KRZYSZTOF KRUPIŃSKI  and
TOMASZ RZEPECKI
KRZYSZTOF KRUPIŃSKI
Affiliation:
INSTYTUT MATEMATYCZNY UNIWERSYTET WROCŁAWSKI PL. GRUNWALDZKI 2/4, 50-384 WROCŁAW POLANDE-mail: kkrup@math.uni.wroc.pl
TOMASZ RZEPECKI
Affiliation:
INSTYTUT MATEMATYCZNY UNIWERSYTET WROCŁAWSKI PL. GRUNWALDZKI 2/4, 50-384 WROCŁAW POLANDE-mail: tomasz.rzepecki@math.uni.wroc.pl
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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.

Keywords

03C4503E1503C60bounded invariant equivalence relationsBorel cardinalitymodel-theoretic connected components

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Type
Articles
Information
The Journal of Symbolic Logic , Volume 81 , Issue 1 , March 2016 , pp. 326 - 356
Copyright
Copyright © The Association for Symbolic Logic 2016 

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References

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