{
  "abstract": "We prove that every acylindrical action on uniformly locally finite product of trees induces the hyperfinite orbit equivalence relation on the Roller boundary. As a byproduct, we construct an example of a standard Borel space and two commuting bounded-to-one surjective partial Borel maps that generate a universal countable Borel equivalence relation. This contrasts to Shinko-Weilacher-Yu's theorem on hyperfiniteness of bounded-to-one actions of commutative monoids.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34068",
  "author_total": 1,
  "authors": [
    {
      "name": "Koichi Oyakawa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8pa1cnm5s6n8z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34068",
  "fulltext_url": null,
  "id": "8pa1cnm5s6n8z",
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  "landing_url": "https://arxiv.org/abs/2609.34068",
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  "licence_label": "arXiv licence",
  "licence_source": "article",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "math.GT"
    ],
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      "arxiv",
      "math.LO"
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      "2608|Advanced Topology and Set Theory"
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  "openalex": "W7214766204",
  "pdf_url": "https://arxiv.org/pdf/2609.34068",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8pa1cnm5s6n8z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.34068",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34068"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Borel complexity for product of trees and commuting partial maps",
  "title_text": "Borel complexity for product of trees and commuting partial maps",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/8pa1cnm5s6n8z",
  "venue": "arXiv",
  "versions": []
}