{
  "abstract": "Rosendal proved that any $K_σ$ equivalence relation is Borel reducible to $\\ell_\\infty$. We prove that for every $F_σ$ equivalence relation $F$ on a Polish space, there is an $F_σ$ real linear subspace $H$ of $\\ell_2$ such that the coset relation $x\\mathrel{E_H}y$ if and only if $x-y\\in H$ has no Baire-measurable reduction to $F$. In particular, there is no $F_σ$ equivalence relation universal under Borel reducibility for all $F_σ$ equivalence relations. This answers a question of Rosendal.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31052",
  "author_total": 1,
  "authors": [
    {
      "name": "Ruijun Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/79mcv84e6exyc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31052",
  "fulltext_url": null,
  "id": "79mcv84e6exyc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31052",
  "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",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7223347589",
  "pdf_url": "https://arxiv.org/pdf/2610.31052",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/79mcv84e6exyc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31052",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31052"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "There is no universal $F_σ$ equivalence relation",
  "title_text": "There is no universal F_σ equivalence relation",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/79mcv84e6exyc",
  "venue": "arXiv",
  "versions": []
}