{
  "abstract": "We consider the Kolchin-generic complete $1$-type of the inviscid Burgers equation $Dx=x\\partial x$ in a differentially closed field of characteristic zero with two commuting derivations. We prove that this type has Lascar rank $1$ and Morley rank $ω$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.18730",
  "author_total": 1,
  "authors": [
    {
      "name": "Piotr Kowalski"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3tcf3qk5pjpvh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.18730",
  "fulltext_url": null,
  "id": "3tcf3qk5pjpvh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.18730",
  "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": "W7213506713",
  "pdf_url": "https://arxiv.org/pdf/2609.18730",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3tcf3qk5pjpvh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:04Z",
      "native_id": "2609.18730",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.18730"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "A minimal type of Morley rank $ω$ in a partial differential field",
  "title_text": "A minimal type of Morley rank ω in a partial differential field",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:04Z",
  "url": "https://research.draconitic.com/paper/3tcf3qk5pjpvh",
  "venue": "arXiv",
  "versions": []
}