{
  "id": "1604.03452",
  "version": "v1",
  "published": "2016-04-12T15:41:50.000Z",
  "updated": "2016-04-12T15:41:50.000Z",
  "title": "Some Infinitary Paradoxes and Undecidable Sentences in Peano Arithmetic",
  "authors": [
    "Ka-Yue Cheng"
  ],
  "comment": "10 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "According to Chaitin, G\\\"odel once told him \"it doesn't matter which paradox you use [to prove the First Incompleteness Theorem]\". In this paper I will present a few infinitary paradoxes and show how to \"translate\" them to some undecidable sentences in Peano arithmetic, like what G\\\"odel did to the Liar paradox. The results partly verify G\\\"odel's claim.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-12T15:41:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03F40"
    ],
    "keywords": [
      "peano arithmetic",
      "infinitary paradoxes",
      "undecidable sentences",
      "first incompleteness theorem",
      "liar paradox"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160403452C"
    }
  }
}