{
  "abstract": "We examine the metamathematical significance of the Levy scheme $Λ$, which asserts, for each natural number $n$, the existence of an $n$-Mahlo cardinal $κ$ such that $V_κ\\prec_{Σ_n}V$. Several initially unrelated constructions single out $\\mathsf{ZFC}+Λ$: comparisons with the model theory of arithmetic and finite set theory; class theories in which the class of ordinals has the tree property; set theories with a proper class of indiscernibles; and interpretations of ordinary set theory in Cantorian parts of models of the extension \\mathsf{NFUA} of Quine--Jensen set theory $\\mathsf{NFU}$. Taken together, the results surveyed here provide a precise sense in which $\\mathsf{ZFC}+Λ$ is an inevitable extension of $\\mathsf{ZFC}$ if one attempts to generalize certain metamathematical results about the microcosm of hereditarily finite sets to the entire macrocosm of sets.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.19283",
  "author_total": 1,
  "authors": [
    {
      "name": "Ali Enayat"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8qrbaks1ye21n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.19283",
  "fulltext_url": null,
  "id": "8qrbaks1ye21n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.19283",
  "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": "W7221970280",
  "pdf_url": "https://arxiv.org/pdf/2610.19283",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8qrbaks1ye21n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.19283",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.19283"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "What David Teaches Goliath: An Inevitable Extension of ZFC",
  "title_text": "What David Teaches Goliath: An Inevitable Extension of ZFC",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/8qrbaks1ye21n",
  "venue": "arXiv",
  "versions": []
}