{
  "id": "2312.17616",
  "version": "v1",
  "published": "2023-12-29T14:23:05.000Z",
  "updated": "2023-12-29T14:23:05.000Z",
  "title": "Interpretations of syntactic fragments of theories of fields",
  "authors": [
    "Sylvy Anscombe",
    "Arno Fehm"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We set up general machinery to study interpretations of fragments of theories. We then apply this to existential fragments of theories of fields, and especially of henselian valued fields. As an application we prove many-one reductions between various existential theories of fields. In particular we exhibit several theories of fields many-one equivalent to the existential theory of $\\mathbb{Q}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-29T14:23:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "12L05",
      "03B25",
      "12J20",
      "03C60",
      "12L05"
    ],
    "keywords": [
      "syntactic fragments",
      "existential theory",
      "fields many-one equivalent",
      "existential fragments",
      "study interpretations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}