{
  "abstract": "We study Borel-Tukey morphisms between almost-homogeneity relations. For finite $r,s\\ge1$ and $m,n\\ge2$, we give the complete one-stage classification: $\\mathbf{Hom}^r_m\\to_{\\mathrm{BT}}\\mathbf{Hom}^s_n$ holds exactly when $r>s$, or when $r=s$ and $m\\ge n$. Our main result is that binary triple homogeneity requires exactly three sequential binary pair stages: $\\mathbf{Hom}^2_2;\\mathbf{Hom}^2_2;\\mathbf{Hom}^2_2\\longrightarrow_{\\mathrm{BT}}\\mathbf{Hom}^3_2$ and $\\mathbf{Hom}^2_2;\\mathbf{Hom}^2_2\\not\\longrightarrow_{\\mathrm{BT}}\\mathbf{Hom}^3_2$. We also construct Borel morphisms $\\mathbf{Hom}^2_2;\\mathbf{Hom}^2_3\\longrightarrow_{\\mathrm{BT}}\\mathbf{Hom}^3_2$ and $\\mathbf{Hom}^2_2;\\mathbf{Hom}^2_2\\longrightarrow_{\\mathrm{BT}}\\mathbf{Hom}^2_k$ for every finite positive $k$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23494",
  "author_total": 1,
  "authors": [
    {
      "name": "Tatsuya Goto"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3aq0brzd0ccf1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23494",
  "fulltext_url": null,
  "id": "3aq0brzd0ccf1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23494",
  "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.LO"
    ],
    [
      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7214039613",
  "pdf_url": "https://arxiv.org/pdf/2609.23494",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3aq0brzd0ccf1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.23494",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23494"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Borel-Tukey morphisms between Ramsey homogeneity relations",
  "title_text": "Borel-Tukey morphisms between Ramsey homogeneity relations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/3aq0brzd0ccf1",
  "venue": "arXiv",
  "versions": []
}