{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08986",
  "author_total": 3,
  "authors": [
    {
      "name": "Ruiyuan Chen"
    },
    {
      "name": "Anush Tserunyan"
    },
    {
      "name": "Robin Tucker-Drob"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fd76zk43cj6gt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08986",
  "fulltext_url": null,
  "id": "fd76zk43cj6gt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08986",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "math.LO"
    ],
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      "openalex",
      "2608|Advanced Topology and Set Theory"
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  "openalex": "W7220912113",
  "pdf_url": "https://arxiv.org/pdf/2610.08986",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fd76zk43cj6gt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.08986",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08986"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Finite index extensions of treeable equivalence relations are treeable",
  "title_text": "Finite index extensions of treeable equivalence relations are treeable",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/fd76zk43cj6gt",
  "venue": "arXiv",
  "versions": []
}