{
  "abstract": "Order-invariant cluster first-order logic (CFO) and local-order-invariant first-order logic are two fragments of order-invariant first-order logic, both motivated by the study of invariant logics on classes of bounded degree. Our main result is that order-invariant CFO contains local-order-invariant FO on arbitrary classes of finite structures, settling the conjecture of Ghasemi and Grange that order-invariant CFO contains plain FO. By combining this with a collapse result of Ghasemi and Grange, we obtain the equivalence of FO, local-order-invariant FO, and order-invariant CFO on classes of finite colored graphs of bounded degree. The proof makes use of Gaifman normal form, which allows our translation from local-order-invariant FO to order-invariant CFO to be effective. Combined with the fixed-parameter tractability of model-checking for order-invariant CFO on bounded-degree colored graph classes, this shows that model-checking for local-order-invariant FO on bounded-degree colored graph classes is fixed-parameter tractable. To generalize our collapse and model-checking results beyond colored graphs, we use a method based on first-order interpretations which also yields a collapse of order-invariant FO to FO when restricted to graph classes of bounded shrub-depth. Finally, we give an application to the database-motivated frozen-witness logic of Abiteboul, Simon, and Vianu by showing that local-order-invariant FO contains deterministic frozen-witness FO, and thus that deterministic frozen-witness FO collapses to FO on classes of finite structures of bounded degree.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01501",
  "author_total": 1,
  "authors": [
    {
      "name": "Derek R. Aoki"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f7zezg12a1c98.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01501",
  "fulltext_url": null,
  "id": "f7zezg12a1c98",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01501",
  "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",
      "cs.LO"
    ],
    [
      "arxiv",
      "math.LO"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01501",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f7zezg12a1c98.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01501",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01501"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Order-Invariant CFO Contains Local-Order-Invariant FO",
  "title_text": "Order-Invariant CFO Contains Local-Order-Invariant FO",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/f7zezg12a1c98",
  "venue": "arXiv",
  "versions": []
}