{
  "id": "2209.07122",
  "version": "v1",
  "published": "2022-09-15T08:10:46.000Z",
  "updated": "2022-09-15T08:10:46.000Z",
  "title": "On Godel's \"Much Weaker\" Assumption",
  "authors": [
    "Saeed Salehi"
  ],
  "comment": "8 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "Godelian sentences of a sufficiently strong and recursively enumerable theory, constructed in Godel's 1931 groundbreaking paper on the incompleteness theorems, are unprovable if the theory is consistent; however, they could be refutable. These sentences are independent when the theory is so-called omega-consistent; a notion introduced by Godel, which is stronger than (simple) consistency, but \"much weaker\" than soundness. Godel goes to great lengths to show in detail that omega-consistency is stronger than consistency, but never shows (or seems to forget to say) why it is much weaker than soundness. In this paper, we study this proof-theoretic notion and compare some of its properties with those of consistency and (variants of) soundness.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-15T08:10:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03F40",
      "03F30"
    ],
    "keywords": [
      "assumption",
      "consistency",
      "godelian sentences",
      "proof-theoretic notion",
      "incompleteness theorems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}