{
  "id": "2410.09195",
  "version": "v1",
  "published": "2024-10-11T18:54:48.000Z",
  "updated": "2024-10-11T18:54:48.000Z",
  "title": "$ω$-consistency for Different Arrays of Quantifiers",
  "authors": [
    "Paulo Guilherme Santos"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We study the formalized v statement by allowing the occurrence of different arrays of quantifiers in it. We prove that for some specific arrays of quantifiers we get consistency statements that are S-equivalent to the original $\\omega$-consistency statement (S denotes the basis theory to develop metamathematics). We end our paper by creating a theory of truth that proves each $\\omega$-consistency-statement.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-11T18:54:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03F03"
    ],
    "keywords": [
      "quantifiers",
      "consistency statement",
      "specific arrays",
      "basis theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}