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arXiv · 2609.21305

Idealistic equivalence relations and the Lusin derivative

Bilge Köksal·Mateusz Lichman·Sławomir Solecki
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Abstract

We give a proof, that does not rely on analytic determinacy, of the existence of an idealistic analytic equivalence relation with Borel classes that is not classwise Borel isomorphic to an orbit equivalence relation. This result answers a question of Becker, and Calderoni and Motto Ros. Our proof proceeds through an analysis of Borel complexity of certain sets of countable rooted trees defined via the notion of the Lusin derivative.

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Bilge Köksal, Mateusz Lichman, Sławomir Solecki. 2026-09-18. Idealistic equivalence relations and the Lusin derivative. https://arxiv.org/abs/2609.21305

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