{
  "id": "1910.01239",
  "version": "v1",
  "published": "2019-10-02T22:12:58.000Z",
  "updated": "2019-10-02T22:12:58.000Z",
  "title": "Undecidability, unit groups, and some totally imaginary infinite extensions of $\\mathbb{Q}$",
  "authors": [
    "Caleb Springer"
  ],
  "comment": "10 pages",
  "categories": [
    "math.NT",
    "math.LO"
  ],
  "abstract": "We produce new examples of totally imaginary infinite extensions of $\\mathbb{Q}$ which have undecidable first-order theory by generalizing the methods used by Martinez-Ranero, Utreras and Videla for $\\mathbb{Q}^{(2)}$. In particular, we use parametrized families of polynomials whose roots are totally real units to apply methods originally developed to prove the undecidability of totally real fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-02T22:12:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11U05"
    ],
    "keywords": [
      "totally imaginary infinite extensions",
      "unit groups",
      "undecidability",
      "totally real fields",
      "undecidable first-order theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}