{
  "abstract": "We show that the first-order theory of the Farey graph is $1$-ample but not $2$-ample. Along the way, we prove that it weakly eliminates imaginaries and observe that forking is trivial.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02427",
  "author_total": 2,
  "authors": [
    {
      "name": "Zahra Mohammadi Khangheshlaghi"
    },
    {
      "name": "Rizos Sklinos"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fk50ntv4hpare.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02427",
  "fulltext_url": null,
  "id": "fk50ntv4hpare",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02427",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.LO"
    ],
    [
      "openalex",
      "2608|Advanced Topology and Set Theory"
    ]
  ],
  "openalex": "W7207563600",
  "pdf_url": "https://arxiv.org/pdf/2609.02427",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fk50ntv4hpare.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02427",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02427"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Ampleness in the Farey graph",
  "title_text": "Ampleness in the Farey graph",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/fk50ntv4hpare",
  "venue": "arXiv",
  "versions": []
}