{
  "abstract": "In this paper, we provide a combinatorial characterization of the elements of Schur ultrafilters on countable commutative groups. Using this characterization, we construct a Schur ultrafilter on $\\mathbb Z$ that is not infinitary Schur. Moreover, assuming the Continuum Hypothesis, we establish the existence of Schur P-points in $β(\\mathbb Z)$. On the other hand, it is consistent with ZFC that there exist P-points in $β(\\mathbb Z)$, but none of them are Schur. Also, we extend the result of Fernández-Bretón, Navarro-Castillo, and Soria-Rojas by showing that no Schur ultrafilter on $\\mathbb Z$ is a Q-point.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.17411",
  "author_total": 1,
  "authors": [
    {
      "name": "S. Bardyla"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a7mys82t9pk43.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.17411",
  "fulltext_url": null,
  "id": "a7mys82t9pk43",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.17411",
  "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.CO"
    ],
    [
      "arxiv",
      "math.LO"
    ],
    [
      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7161701495",
  "pdf_url": "https://arxiv.org/pdf/2605.17411",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a7mys82t9pk43.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2605.17411",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.17411"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Combinatorics of Schur ultrafilters",
  "title_text": "Combinatorics of Schur ultrafilters",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/a7mys82t9pk43",
  "venue": "arXiv",
  "versions": []
}