{
  "id": "math/0501421",
  "version": "v1",
  "published": "2005-01-24T18:55:44.000Z",
  "updated": "2005-01-24T18:55:44.000Z",
  "title": "Some partition properties for measurable colourings of omega-one^2",
  "authors": [
    "James Hirschorn"
  ],
  "comment": "Proceedings of the Kyoto conference on Forcing Method and Large Cardinals, 2004",
  "categories": [
    "math.LO",
    "math.CA"
  ],
  "abstract": "We construct a measure on omega-one^2 over the ground model in the forcing extension of a measure algebra, and investigate when measure theoretic properties of some measurable colouring of omega-one^2 imply the existence of an uncountable subset of omega-one whose square is homogeneous. This gives a new proof of the fact that, under a suitable axiomatic assumption, there are no Souslin (omega-one,omega-one) gaps in the Boolean algebra L^0(nu)/Fin when nu is a separable measure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-01-24T18:55:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "partition properties",
      "measurable colouring",
      "measure theoretic properties",
      "measure algebra",
      "ground model"
    ],
    "tags": [
      "conference paper"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......1421H"
    }
  }
}