{
  "abstract": "After defining the concept of inevitability for statements with the modal logic of forcing, we raise the question of which statements are inevitable under $\\mathsf{ZFC}$ and under large cardinal hypotheses. We show that $\\mathsf{SOA}$ (defined as $\\mathsf{ZFC}^-$ + $\\mathsf V=\\mathsf{HC}$) plus the $\\boldsymbolΣ^1_2$-perfect set property is $\\mathsf{ZFC}$-inevitable, and that Projective Determinacy is inevitable in the theory of $\\mathsf{ZFC}$ with a proper class of Woodin cardinals. We then discuss the possible conceptual significance of these results for the foundations of set theory.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.31040",
  "author_total": 2,
  "authors": [
    {
      "name": "Chris Scambler"
    },
    {
      "name": "Cesare Straffelini"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a8x46vpa4fgez.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.31040",
  "fulltext_url": null,
  "id": "a8x46vpa4fgez",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.31040",
  "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": "W7223331954",
  "pdf_url": "https://arxiv.org/pdf/2610.31040",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a8x46vpa4fgez.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.31040",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.31040"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Set-theoretic inevitability",
  "title_text": "Set-theoretic inevitability",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/a8x46vpa4fgez",
  "venue": "arXiv",
  "versions": []
}