{
  "id": "1804.03798",
  "version": "v1",
  "published": "2018-04-11T03:47:59.000Z",
  "updated": "2018-04-11T03:47:59.000Z",
  "title": "Developing Takeuti-Yasumoto forcing",
  "authors": [
    "Satoru Kuroda"
  ],
  "comment": "17 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "In late 90's G.Takeuti and Y.Yasumoto gave forcing constructions for bounded arithmetic. We will reformulate their constructions using two-sort bounded arithmetic and prove the followings. 1. Generic extensions are related with P=NP problem. 2. J.Krajicek's forcing constructions can be given as Takeuti-Yasumoto forcing. 3. We can either satisfy or falsify the dual weak pigeonhole principles in generic extensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-11T03:47:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "developing takeuti-yasumoto forcing",
      "generic extensions",
      "dual weak pigeonhole principles",
      "yasumoto gave forcing constructions",
      "two-sort bounded arithmetic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}