{
  "abstract": "We construct a sentence of $L_{ω_1,ω}$ having exactly $\\aleph_1$ many countable models up to isomorphism, but no perfect set of non-isomorphic models. This disproves Vaught's conjecture for infinitary logic. The construction follows a framework devised by Robin Knight, and the proof has been formally verified in Lean.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15217",
  "author_total": 3,
  "authors": [
    {
      "name": "Nathanael L. Ackerman"
    },
    {
      "name": "Cameron E. Freer"
    },
    {
      "name": "Robin W. Knight"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4bjzcd0s697sg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15217",
  "fulltext_url": null,
  "id": "4bjzcd0s697sg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15217",
  "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": "W7221766611",
  "pdf_url": "https://arxiv.org/pdf/2610.15217",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4bjzcd0s697sg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15217",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15217"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "A counterexample to Vaught's Conjecture for $L_{ω_1,ω}$",
  "title_text": "A counterexample to Vaught's Conjecture for L_ω_1,ω",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/4bjzcd0s697sg",
  "venue": "arXiv",
  "versions": []
}