{
  "id": "1609.07872",
  "version": "v1",
  "published": "2016-09-26T07:20:10.000Z",
  "updated": "2016-09-26T07:20:10.000Z",
  "title": "Every linear order isomorphic to its cube is isomorphic to its square",
  "authors": [
    "Garrett Ervin"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "In 1958, Sierpi\\'nski asked whether there exists a linear order $X$ that is isomorphic to its lexicographically ordered cube but is not isomorphic to its square. The main result of this paper is that the answer is negative. More generally, if $X$ is isomorphic to any one of its finite powers $X^n$, $n>1$, it is isomorphic to all of them.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-26T07:20:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "linear order isomorphic",
      "main result",
      "finite powers",
      "sierpinski"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}