{
  "abstract": "If α and β are cardinals, then the cardinal exponentiation αβ is the set of all functions from α into β. The ABCD hypothesis is the statement that for all infinite cardinals α≤β and γ≤δ, |αβ|≤|γδ| if and only if α≤γ and β≤δ. The Axiom of Determinacy, AD, states that every two-player infinite game on ω has a winning strategy for one of the two players. Let Θ be the supremum of the ordinals onto which R surjects. This paper will show that if AD holds and V=L(R), then the ABCD hypothesis holds below Θ.",
  "abstract_shown": true,
  "affiliations": [
    "Institut für diskrete Mathematik und Geometrie, Technische Universität Wien, Vienna 1040, Austria"
  ],
  "article_type": "research article",
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "William Chan",
      "orcid": "0000-0002-0661-1764"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fkq8rm2hwxcs2.bib",
  "cited_by": 0,
  "doi": "10.1073/pnas.2621223123",
  "fulltext_url": "https://pmc.ncbi.nlm.nih.gov/articles/PMC13732085/",
  "id": "fkq8rm2hwxcs2",
  "issns": [
    "0027-8424",
    "1091-6490"
  ],
  "landing_url": "https://doi.org/10.1073/pnas.2621223123",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "heading",
      "421"
    ],
    [
      "heading",
      "Mathematics"
    ],
    [
      "heading",
      "Physical Sciences"
    ],
    [
      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7224597959",
  "pdf_url": null,
  "pmcid": "PMC13732085",
  "pmid": "42956038",
  "published": "2026-10-29",
  "publisher": "National Academy of Sciences",
  "ris": "https://research.draconitic.com/paper/fkq8rm2hwxcs2.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T12:22:08Z",
      "native_id": "PMC13732085",
      "source": "pmc",
      "url": "https://doi.org/10.1073/pnas.2621223123"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Advanced Topology and Set Theory",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The ABCD hypothesis",
  "title_text": "The ABCD hypothesis",
  "type": "peer-reviewed",
  "updated_at": "2026-11-08T12:22:08Z",
  "url": "https://research.draconitic.com/paper/fkq8rm2hwxcs2",
  "venue": "Proceedings of the National Academy of Sciences of the United States of America",
  "versions": []
}