{
  "abstract": "We show that unlike $\\textsf{PFA}$, $\\textsf{MA}_{ω_{1}}$ is consistent with the existence of $2^{ω_{1}}$-many Countryman lines which pairwise contain no uncountable isomorphic or reverse-isomorphic suborders. This clarifies an issue regarding the claim that $\\textsf{MA}_{ω_{1}}$ implies that there is a finite basis for the Countryman lines. The family of Countryman lines comes from a family of $2^{ω_{1}}$-many coherent trees which pairwise contain no club-isomorphic subtrees. To prove this, we first construct such a family of trees using $\\diamondsuit$, and then we iterate ccc forcings while preserving this property.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05582",
  "author_total": 1,
  "authors": [
    {
      "name": "Lucas Polymeris"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dpe1n19vc3ber.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05582",
  "fulltext_url": null,
  "id": "dpe1n19vc3ber",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05582",
  "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": "W7220712472",
  "pdf_url": "https://arxiv.org/pdf/2610.05582",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dpe1n19vc3ber.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05582",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05582"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Countryman basis and club-isomorphisms under MA$(ω_1)$",
  "title_text": "Countryman basis and club-isomorphisms under MA(ω_1)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/dpe1n19vc3ber",
  "venue": "arXiv",
  "versions": []
}