{
  "abstract": "A \\emph{Johnson graph} $J(n,k)$ is a graph whose vertices are the $k$-element subsets of an underlying set of size $n$ where two vertices are adjacent if they intersect in a subset of size $k-1$. We extend the definition to allow infinite parameters and we study a natural limit theory $T_{\\mathcal{J}}$ of Johnson graphs. We show that $T_{\\mathcal{J}}$ is complete and we give an axiomatisation of $T_{\\mathcal{J}}$, from which we obtain a complete description of the models of $T_{\\mathcal{J}}$. We use this to show tameness properties of $T_{\\mathcal{J}}$, namely that $T_{\\mathcal{J}}$ is $ω$-stable of Morley rank $ω$, but not monadically dependent. In particular it follows that the class of all finite Johnson graphs is stable, and therefore dependent but not monadically dependent.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40054",
  "author_total": 3,
  "authors": [
    {
      "name": "Bjarki Geir Benediktsson"
    },
    {
      "name": "Dugald Macpherson"
    },
    {
      "name": "Isolde Adler"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7561x2epbn0hb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40054",
  "fulltext_url": null,
  "id": "7561x2epbn0hb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40054",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.LO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40054",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7561x2epbn0hb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.40054",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40054"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Model Theory of Johnson Graphs",
  "title_text": "Model Theory of Johnson Graphs",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/7561x2epbn0hb",
  "venue": "arXiv",
  "versions": []
}