{
  "id": "2310.17862",
  "version": "v1",
  "published": "2023-10-27T02:30:41.000Z",
  "updated": "2023-10-27T02:30:41.000Z",
  "title": "A model theoretic proof for o-minimal coherence theorem",
  "authors": [
    "Yayi Fu"
  ],
  "categories": [
    "math.LO",
    "math.CV"
  ],
  "abstract": "Bakker, Brunebarbe, Tsimerman showed in \\cite{bakker2022minimal} that the definable structure sheaf $\\mathcal{O}_{\\mathbb{C}^n}$ of $\\mathbb{C}^n$ is a coherent $\\mathcal{O}_{\\mathbb{C}^n}$-module as a sheaf on the site $\\underline{\\mathbb{C}^n}$, where the coverings are finite coverings by definable open sets. In general, let $\\mathbb{K}$ be an algebraically closed field of characteristic zero. We give a more model-theoretic proof of the coherence of $\\mathcal{O}_{\\mathbb{K}^n}$ as a sheaf of $\\mathcal{O}_{\\mathbb{K}^n}$-module on the site $\\underline{\\mathbb{K}^n}$ using spectral topology on the type space $S_n(\\mathbb{K})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-27T02:30:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "model theoretic proof",
      "o-minimal coherence theorem",
      "spectral topology",
      "model-theoretic proof",
      "characteristic zero"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}