{
  "id": "math/0603260",
  "version": "v1",
  "published": "2006-03-12T19:36:53.000Z",
  "updated": "2006-03-12T19:36:53.000Z",
  "title": "Large cardinals with few measures",
  "authors": [
    "Arthur W. Apter",
    "James Cummings",
    "Joel David Hamkins"
  ],
  "comment": "15 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We show, assuming the consistency of one measurable cardinal, that it is consistent for there to be exactly kappa+ many normal measures on the least measurable cardinal kappa. This answers a question of Stewart Baldwin. The methods generalize to higher cardinals, showing that the number of lambda strong compactness or lambda supercompactness measures on P_kappa(lambda) can be exactly lambda+, if lambda>kappa is a regular cardinal. We conclude with a list of open questions. Our proofs use a critical observation due to James Cummings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-03-12T19:36:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E35",
      "03E55"
    ],
    "keywords": [
      "large cardinals",
      "lambda supercompactness measures",
      "lambda strong compactness",
      "regular cardinal",
      "normal measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......3260A"
    }
  }
}