{
  "id": "1306.1794",
  "version": "v1",
  "published": "2013-06-07T17:51:52.000Z",
  "updated": "2013-06-07T17:51:52.000Z",
  "title": "Some supplements to Feferman-Vaught related to the model theory of adeles",
  "authors": [
    "Jamshid Derakhshan",
    "Angus Macintyre"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We give foundational results for the model theory of the ring of finite adeles over a number field, construed as a restricted product of local fields. In contrast to Weispfenning we work in the language of ring theory, and various sortings interpretable therein. In particular we give a systematic treatment of the product valuation and the valuation monoid. Deeper results are given for the adelic version of Krasner's hyperfields, relating them to the Basarab-Kuhlmann formalism.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-07T17:51:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C10",
      "03C40",
      "03C60",
      "03C95",
      "03C98",
      "11U05",
      "11U09",
      "12L05",
      "12L12",
      "12E50"
    ],
    "keywords": [
      "model theory",
      "feferman-vaught",
      "supplements",
      "foundational results",
      "finite adeles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.1794D"
    }
  }
}