{
  "abstract": "We prove that the family of coset relations of $F_σ$ real linear subspaces of Banach space $\\ell_1$ has no common upper bound among Borel equivalence relations in the sense of Borel reducibility. These relations are indexed by a well-founded tree. Consequently, on a Polish space, a universal $Σ^0_α$ equivalence relation exists exactly when $α=1$, and a universal $Π^0_α$ equivalence relation exists exactly when $α=1$ or $2$. This strengthens the earlier nonexistence theorem for a universal $F_σ$ equivalence relation. This also answers a question of Kanovei and Lyubetsky about universal equivalence relations in Borel classes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.02531",
  "author_total": 1,
  "authors": [
    {
      "name": "Ruijun Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f0vfdm2vk9kze.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.02531",
  "fulltext_url": null,
  "id": "f0vfdm2vk9kze",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.02531",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.LO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.02531",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f0vfdm2vk9kze.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.02531",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.02531"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "No Borel upper bound for the $F_σ$ equivalence relations",
  "title_text": "No Borel upper bound for the F_σ equivalence relations",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/f0vfdm2vk9kze",
  "venue": "arXiv",
  "versions": []
}