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PreprintarXiv licencearXiv

Finite index extensions of treeable equivalence relations are treeable

  • Ruiyuan Chen
  • Anush Tserunyan
  • Robin Tucker-Drob
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Abstract

We prove that every countable Borel equivalence relation containing a finite index Borel treeable subequivalence relation is Borel treeable. This answers a long-standing question of Jackson--Kechris--Louveau. Our proof is based on a median subalgebra filtration construction on products of trees, together with an extension of the median graph treeing algorithm of Chen--Poulin--Tao--Tserunyan to certain well-behaved increasing unions.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026finite,
  title = {{Finite index extensions of treeable equivalence relations are treeable}},
  author = {Ruiyuan Chen and Anush Tserunyan and Robin Tucker-Drob},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.08986},
  eprint = {2610.08986},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.08986},
}
RIS
TY  - UNPB
TI  - Finite index extensions of treeable equivalence relations are treeable
AU  - Ruiyuan Chen
AU  - Anush Tserunyan
AU  - Robin Tucker-Drob
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.08986
UR  - https://arxiv.org/abs/2610.08986
AB  - We prove that every countable Borel equivalence relation containing a finite index Borel treeable subequivalence relation is Borel treeable. This answers a long-standing question of Jackson--Kechris--Louveau. Our proof is based on a median subalgebra filtration construction on products of trees, together with an extension of the median graph treeing algorithm of Chen--Poulin--Tao--Tserunyan to certain well-behaved increasing unions.
ER  -