{
  "id": "2203.06322",
  "version": "v1",
  "published": "2022-03-12T02:43:42.000Z",
  "updated": "2022-03-12T02:43:42.000Z",
  "title": "A Simple Combinatorial Proof of Szemerédi's Theorem via Three Levels of Infinities",
  "authors": [
    "Renling Jin"
  ],
  "categories": [
    "math.LO",
    "math.CO",
    "math.NT"
  ],
  "abstract": "We present a nonstandard simple elementary proof of Szemer\\'{e}di's theorem by a straightforward induction with the help of three levels of infinities and four different elementary embeddings in a nonstandard universe.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-12T02:43:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C98",
      "11B25"
    ],
    "keywords": [
      "simple combinatorial proof",
      "szemerédis theorem",
      "infinities",
      "nonstandard simple elementary proof",
      "elementary embeddings"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}