{
  "id": "2208.08293",
  "version": "v1",
  "published": "2022-08-17T13:47:30.000Z",
  "updated": "2022-08-17T13:47:30.000Z",
  "title": "On definable groups in real closed fields with a generic derivation, and related structures: I",
  "authors": [
    "Ya'acov Peterzil",
    "Anand Pillay",
    "Francoise Point"
  ],
  "comment": "39 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We study finite-dimensional groups definable in models of the theory of real closed fields with a generic derivation (also known as CODF). We prove that any such group definably embeds in a semialgebraic group. We extend the results to several more general contexts; strongly model complete theories of large geometric fields with a generic derivation, model complete o-minimal expansions of RCF with a generic derivation, open theories of topological fields with a generic derivation. We also give a general theorem on recovering a definable group from generic data in the context of geometric structures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-17T13:47:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C60",
      "03C64",
      "12H05",
      "14L10",
      "14P10"
    ],
    "keywords": [
      "generic derivation",
      "real closed fields",
      "definable group",
      "related structures",
      "model complete o-minimal expansions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}