{
  "abstract": "Motivated by the existence of closed maximal $\\mathcal{I}$-eventually different ($\\mathcal{I}$-MED) families, we study uniform combinatorial properties of ideals. For a fixed ideal, a property is uniform if its witnesses can be chosen by a single Borel map. We prove that every $\\boldsymbolΣ^0_3$ ideal is uniformly weakly $P^+$. We also prove that the classes of Farah and weakly Farah ideals coincide, answering a question of Hrušák and Meza-Alcántara. We then show that every weakly Farah ideal is uniformly weakly Ramsey. As an application, we obtain closed $\\mathcal{I}$-MED families for $\\boldsymbolΣ^0_3$ ideals and weakly Farah ideals.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28275",
  "author_total": 3,
  "authors": [
    {
      "name": "Jialiang He"
    },
    {
      "name": "Jiaheng Zhuang"
    },
    {
      "name": "Yi Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7gh10dt0ne4a2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28275",
  "fulltext_url": null,
  "id": "7gh10dt0ne4a2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28275",
  "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": "W7223098559",
  "pdf_url": "https://arxiv.org/pdf/2610.28275",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7gh10dt0ne4a2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.28275",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28275"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Closed maximal eventually different families for $\\boldsymbolΣ^0_3$ and weakly Farah ideals",
  "title_text": "Closed maximal eventually different families for Σ^0_3 and weakly Farah ideals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/7gh10dt0ne4a2",
  "venue": "arXiv",
  "versions": []
}