{
  "id": "1601.08214",
  "version": "v1",
  "published": "2016-01-29T18:06:17.000Z",
  "updated": "2016-01-29T18:06:17.000Z",
  "title": "Slow Reflection",
  "authors": [
    "Anton Freund"
  ],
  "comment": "25 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We describe a \"slow\" version of the hierarchy of uniform reflection principles over Peano Arithmetic. These principles are unprovable in Peano Arithmetic (even when extended by usual reflection principles of lower complexity) and introduce a new provably total function. At the same time the consistency of $\\mathbf{PA}$ plus slow reflection is provable in $\\mathbf{PA}+\\text{Con}(\\mathbf{PA})$. We deduce a conjecture of S.-D. Friedman, Rathjen and Weiermann: Transfinite iterations of slow consistency generate a hierarchy of precisely $\\varepsilon_0$ stages between $\\mathbf{PA}$ and $\\mathbf{PA}+\\text{Con}(\\mathbf{PA})$ (where $\\text{Con}(\\mathbf{PA})$ refers to the usual consistency statement).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-29T18:06:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03F25",
      "03F30",
      "03C62"
    ],
    "keywords": [
      "peano arithmetic",
      "usual reflection principles",
      "uniform reflection principles",
      "plus slow reflection",
      "slow consistency generate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160108214F"
    }
  }
}