{
  "id": "1907.03737",
  "version": "v1",
  "published": "2019-07-08T17:41:30.000Z",
  "updated": "2019-07-08T17:41:30.000Z",
  "title": "Easton's theorem for the tree property below aleph_omega",
  "authors": [
    "Sarka Stejskalova"
  ],
  "comment": "24 pages, submitted",
  "categories": [
    "math.LO"
  ],
  "abstract": "Starting with infinitely many supercompact cardinals, we show that the tree property at every cardinal $\\aleph_n$, $1 < n <\\omega$, is consistent with an arbitrary continuum function below $\\aleph_\\omega$ which satisfies $2^{\\aleph_n} > \\aleph_{n+1}$, $n<\\omega$. Thus the tree property has no provable effect on the continuum function below $\\aleph_\\omega$ except for the restriction that the tree property at $\\kappa^{++}$ implies $2^\\kappa>\\kappa^+$ for every infinite $\\kappa$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-08T17:41:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tree property",
      "eastons theorem",
      "arbitrary continuum function",
      "supercompact cardinals",
      "consistent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}