{
  "abstract": "We obtain a strong decomposition theorem for invariant global types in a monadically NIP theory. From this, we prove that if an $n$-type $tp(\\bar{a}/MC)$ does not fork over $M$ then $\\bar{a}=(\\bar{f},\\bar{d})$ where $tp(\\bar{d}/MC)$ is $M$-definable and $tp(\\bar{f}/MC\\bar{d})$ is finitely satisfied in $M$. Over arbitrary base sets $B$, we prove that an $n$-type $tp(\\bar{a}/BC)$ does not fork over $B$ if and only if $tp(a_i/BC)$ does not fork over $B$ for each singleton $a_i\\in\\bar{a}$. We show that monadically NIP theories satisfy density of definable types among non-forking extensions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25129",
  "author_total": 1,
  "authors": [
    {
      "name": "Michael C. Laskowski"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d9nbc72j70b1k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25129",
  "fulltext_url": null,
  "id": "d9nbc72j70b1k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25129",
  "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": "W7214068035",
  "pdf_url": "https://arxiv.org/pdf/2609.25129",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d9nbc72j70b1k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25129",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25129"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Forking and invariant types in monadic NIP theories",
  "title_text": "Forking and invariant types in monadic NIP theories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/d9nbc72j70b1k",
  "venue": "arXiv",
  "versions": []
}