{
  "id": "2405.12771",
  "version": "v1",
  "published": "2024-05-21T13:23:14.000Z",
  "updated": "2024-05-21T13:23:14.000Z",
  "title": "Universal-existential theories of fields",
  "authors": [
    "Sylvy Anscombe",
    "Arno Fehm"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We study various universal-existential fragments of first-order theories of fields, in particular of function fields and of equicharacteristic henselian valued fields. For example we discuss to what extent the theory of a field k determines the universal-existential theories of the rational function field over k and of the field of Laurent series over k, and we find various many-one reductions between such fragments.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-21T13:23:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C60",
      "12L05",
      "12L12",
      "12J20",
      "14H05"
    ],
    "keywords": [
      "universal-existential theories",
      "equicharacteristic henselian valued fields",
      "rational function field",
      "universal-existential fragments",
      "first-order theories"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}