PreprintCC BY 4.0arXiv
Idealistic equivalence relations and the Lusin derivative
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.
Related
- Realizations of Countable Borel Equivalence Relations
- Finite-index extensions of essentially free countable Borel equivalence relations
- Finite index extensions of treeable equivalence relations are treeable
- No Borel upper bound for the Fσ equivalence relations
- Ergodic treeable equivalence relations are richly ergodic
BibTeX
@misc{koksal2026idealistic,
title = {{Idealistic equivalence relations and the Lusin derivative}},
author = {Bilge Köksal and Mateusz Lichman and Sławomir Solecki},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21305},
eprint = {2609.21305},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21305},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Idealistic equivalence relations and the Lusin derivative
AU - Bilge Köksal
AU - Mateusz Lichman
AU - Sławomir Solecki
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21305
UR - https://arxiv.org/abs/2609.21305
AB - 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.
ER -