{
  "id": "1902.07373",
  "version": "v1",
  "published": "2019-02-20T02:09:58.000Z",
  "updated": "2019-02-20T02:09:58.000Z",
  "title": "Construction and Set Theory",
  "authors": [
    "Andrew Powell"
  ],
  "comment": "6 pages, no figures. Experimental paper; comments welcome",
  "categories": [
    "math.LO"
  ],
  "abstract": "This paper argues that mathematical objects are constructions and that constructions introduce a flexibility in the ways that mathematical objects are represented (as sets of binary sequences for example) and presented (in a particular order for example). The construction approach is then applied to searching for a mathematical object in a set, and a logarithm-time search algorithm outlined which applies to a set X of all binary sequences of length ordinal $\\beta$ with a binary label appended to each sequence to indicate that sequence is a member of X or not. It follows that deciding membership of a set of binary sequences of length ordinal $\\beta$ takes $\\beta+1$ bits, which is shown to be equivalent to the Generalised Continuum Hypothesis.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-20T02:09:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "set theory",
      "binary sequences",
      "mathematical object",
      "length ordinal",
      "logarithm-time search algorithm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}