{
  "id": "math/0605448",
  "version": "v2",
  "published": "2006-05-16T18:32:50.000Z",
  "updated": "2006-05-16T20:04:00.000Z",
  "title": "Scales and the fine structure of K(R). Part II: Weak real mice and scales",
  "authors": [
    "D. W. Cunningham"
  ],
  "comment": "27 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We define weak real mice $\\mathcal{M}$ and prove that the boldface pointclass $\\boldsymbol{\\Sigma}_m(\\mathcal{M})$ has the scale property assuming only the determinacy of sets of reals in $\\mathcal{M}$ when $m$ is the smallest integer $m>0$ such that $\\boldsymbol{\\Sigma}_m(\\mathcal{M})$ contains a set of reals not in $\\mathcal{M}$. We shall use this development in Part III to obtain scales of minimal complexity in $K(\\mathbb{R})$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-05-16T20:04:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E15",
      "03E45",
      "03E60"
    ],
    "keywords": [
      "fine structure",
      "define weak real mice",
      "minimal complexity",
      "smallest integer",
      "boldface pointclass"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......5448C"
    }
  }
}