{
  "id": "2004.05593",
  "version": "v1",
  "published": "2020-04-12T12:01:51.000Z",
  "updated": "2020-04-12T12:01:51.000Z",
  "title": "A note on the non-existence of prime models of theories of pseudo-finite fields",
  "authors": [
    "Zoé Chatzidakis"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We show that if a field A is not pseudo-finite, then there is no prime model of the theory of pseudo-finite fields over A. Assuming GCH, we generalise this result to \\kappa-prime models, for \\kappa a regular uncountable cardinal or \\aleph_\\epsilon.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-12T12:01:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C50",
      "03C60",
      "12L12",
      "12E20"
    ],
    "keywords": [
      "pseudo-finite fields",
      "prime model",
      "non-existence",
      "regular uncountable cardinal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}