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arXiv · 2609.02997

Finite-index extensions of essentially free countable Borel equivalence relations

Jason Zesheng Chen
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Abstract

Kechris asked whether essential freeness of countable Borel equivalence relations is preserved under extensions of finite index. Kaya proved that every such extension of a relation $E$ is Borel reducible to the equivalence relation $E^{\mathrm{fin}}$ on nonempty finite subsets which records the $E$-classes met by the subset. We show that $E^{\mathrm{fin}}$ is essentially free whenever $E$ is. This gives an affirmative answer to Kechris's question.

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Jason Zesheng Chen. 2026-09-02. Finite-index extensions of essentially free countable Borel equivalence relations. https://arxiv.org/abs/2609.02997

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