{
  "abstract": "An ideal $\\mathcal{I}$ on $ω$ is called Farah if there are hereditary closed subsets $C_n$ of $\\mathcal{P}(ω)$, for $n\\inω$, such that $\\mathcal{I}=\\{A\\subseteqω:\\ \\forall_{n\\inω}\\ \\exists_{k\\inω}\\ A\\setminus k\\in C_n\\}$. Farah asked in [Trans. Amer. Math. Soc. 356 (2004), no. 6] if every $\\mathbf{F_{σδ}}$ ideal is a Farah ideal. We show that this is false by providing both tall and non-tall counterexamples. Moreover, we show that there is an antichain in the sense of Katětov order of length $\\continuum$ consisting of $\\mathbf{F_{σδ}}$ non-Farah ideals. We also investigate a closely related problem concerning sets of ideal limit points. We show that if $\\mathcal{I}$ is an $\\mathbf{G_{δσδ}}$ ideal on $ω$ and $x\\in X^ω$ is a sequence in an uncountable Polish space $X$, then \\[ Λ_x(\\mathcal{I})=\\left\\{p\\in X:\\ \\exists_{A\\notin\\mathcal{I}}\\ x\\restriction A\\text{ converges to }p\\right\\} \\] is $\\mathbf{F_σ}$. This answers [Top. App. 312 (2022)] (partially) and [J. Symb. Logic, DOI: 10.1017/jsl.2026.10181]. Earlier it was known to be true only in the case of Farah ideals.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03432",
  "author_total": 1,
  "authors": [
    {
      "name": "Adam Kwela"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0sky5dqcw5s4y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03432",
  "fulltext_url": null,
  "id": "0sky5dqcw5s4y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03432",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03432",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0sky5dqcw5s4y.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03432",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03432"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "On Farah ideals and beyond",
  "title_text": "On Farah ideals and beyond",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/0sky5dqcw5s4y",
  "venue": "arXiv",
  "versions": []
}