{
  "abstract": "We propose a new variant of Vaught's conjecture, based on Martin's (model-theoretic) conjecture and the $ω$-Vaught's conjecture of Gonzalez and Montalbán. For $ω$-stable theories, we prove the conjecture by analyzing in detail Bouscaren's and Shelah-Harrington-Makkai's proofs of Martin's conjecture and Vaught's conjecture, respectively, for $ω$-stable theories. In particular, when there are countably many countable models, we improve the required number of quantifiers for a Scott sentence from $ω+ω$ to $ω+5$, and we obtain a similar bound of $ω+6$ for the uncountable case.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09314",
  "author_total": 1,
  "authors": [
    {
      "name": "Hongyu Zhu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4kftndj9t9x8f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09314",
  "fulltext_url": null,
  "id": "4kftndj9t9x8f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09314",
  "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": "W7220916947",
  "pdf_url": "https://arxiv.org/pdf/2610.09314",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4kftndj9t9x8f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.09314",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09314"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "The Type $ω$-Vaught's Conjecture for $ω$-stable Theories",
  "title_text": "The Type ω-Vaught's Conjecture for ω-stable Theories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/4kftndj9t9x8f",
  "venue": "arXiv",
  "versions": []
}