{
  "id": "1811.12603",
  "version": "v1",
  "published": "2018-11-30T04:05:06.000Z",
  "updated": "2018-11-30T04:05:06.000Z",
  "title": "Hamel Spaces and Distal Expansions",
  "authors": [
    "Allen Gehret",
    "Travis Nell"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "In this note, we construct a distal expansion for the structure $(\\mathbb{R}; +,<,H)$, where $H\\subseteq \\mathbb{R}$ is a dense $\\mathbb{Q}$-vector space basis of $\\mathbb{R}$ (a so-called Hamel basis). Our construction is also an expansion of the dense pair $(\\mathbb{R}; +,<,\\mathbb{Q})$ and has full quantifier elimination in a natural language.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-30T04:05:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C64",
      "03C45"
    ],
    "keywords": [
      "distal expansion",
      "hamel spaces",
      "full quantifier elimination",
      "vector space basis",
      "natural language"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}