{
  "abstract": "This paper shows that the pairwise intersection principle ($2\\mathrm{IP}$) implies, over $\\mathsf{RCA}_0$, the existence of a Cohen $1$-generic real relative to every given set. Together with the known implications, this yields the equivalence over $\\mathsf{RCA}_0$ of the finite intersection principle (FIP), $2\\mathrm{IP}$, and $1$-GEN. In fact, FIP is equivalent to $n\\mathrm{IP}$ for every fixed $n\\geq 2$. These results give affirmative answers to Questions~1 and~2 of Cholak, Downey, and Igusa, and to Question~9.10.26 of Dzhafarov and Mummert. The proof uses cumulative, nested supports satisfying a finite Helly property and a decoding argument based on a least selected label. Neither $Σ^0_2$ induction nor $Σ^0_2$ bounding is required.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01571",
  "author_total": 1,
  "authors": [
    {
      "name": "Patrizio Cintioli"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/frp5c46cnpy8m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01571",
  "fulltext_url": null,
  "id": "frp5c46cnpy8m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01571",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.LO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01571",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/frp5c46cnpy8m.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01571",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01571"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "$\\mathsf{RCA}_0$ Proves the Collapse of the Intersection Principles Hierarchy",
  "title_text": "RCA_0 Proves the Collapse of the Intersection Principles Hierarchy",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/frp5c46cnpy8m",
  "venue": "arXiv",
  "versions": []
}