{
  "abstract": "We study the countable partition model over a set of atoms of arbitrary uncountable cardinality $κ$. Its supports are partitions of the atoms into countably many blocks, and a permutation fixes a support when it preserves each block setwise. This model was proposed by Bruce and studied by Banerjee. We prove that dependent choice holds for every $κ$, although the filter of subgroups is not closed under countable intersections. Choice for well-orderable families holds exactly when $κ<\\aleph_{ω_1}$; when $κ\\ge\\aleph_{ω_1}$, an $ω_1$-indexed family witnesses its failure. The Hartogs and Lindenbaum numbers of the set of atoms are both $ω_1$. The proofs use permutations matching blocks of equal cardinality and establish shift completeness of the filter. Together with Banerjee's failure of $\\mathsf{DC}_{ω_1}$, these results determine which dependent choice principles hold in the model.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29752",
  "author_total": 1,
  "authors": [
    {
      "name": "Brinda Venkataramani"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4d000dqkzjvzv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29752",
  "fulltext_url": null,
  "id": "4d000dqkzjvzv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29752",
  "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": "W7223221823",
  "pdf_url": "https://arxiv.org/pdf/2610.29752",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4d000dqkzjvzv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29752",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29752"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Choice principles in countable partition models",
  "title_text": "Choice principles in countable partition models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/4d000dqkzjvzv",
  "venue": "arXiv",
  "versions": []
}