{
  "id": "1202.5799",
  "version": "v3",
  "published": "2012-02-26T22:45:17.000Z",
  "updated": "2017-01-18T21:31:33.000Z",
  "title": "A parallel to the null ideal for inaccessible lambda. Part I",
  "authors": [
    "Saharon Shelah"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "It is well known to generalize the meagre ideal replacing aleph_0 by a (regular) cardinal lambda > aleph_0 and requiring the ideal to be lambda^+-complete. But can we generalize the null ideal? In terms of forcing, this means finding a forcing notion similar to the random real forcing, replacing aleph_0 by lambda, so requiring it to be (<lambda)-complete. Of course, we would welcome additional properties generalizing the ones of the random real forcing. Returning to the ideal (instead forcing) we may look at the Boolean Algebra of lambda-Borel sets modulo the ideal. Surprisingly we get an positive = existence answer for lambda a \"mild\" large cardinals: the weakly compact ones. We apply this to get consistency results on cardinal invariants for such lambda's. We shall deal with other cardinals more properties related forcing notions in a continuation.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-06-09T23:17:42.000Z",
      "title": "A parallel to the null ideal for inaccessible lambda",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2017-01-18T21:31:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "null ideal",
      "inaccessible lambda",
      "random real forcing",
      "lambda-borel sets modulo",
      "properties related forcing notions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1202.5799S"
    }
  }
}