{
  "id": "1501.03649",
  "version": "v1",
  "published": "2015-01-15T12:39:06.000Z",
  "updated": "2015-01-15T12:39:06.000Z",
  "title": "Preservation properties for iterations with finite support",
  "authors": [
    "Diego Alejandro Mejía"
  ],
  "comment": "Included in the proceedings of RIMS Set Theory Workshop on reflection principles and set theory of large cardinals, Kyoto, Japan (2013 Sep). 11 pages",
  "journal": "Kyoto Daigaku Suurikaiseki Kenkyuusho Koukyuuroku 1895 (2014) 68-78",
  "categories": [
    "math.LO"
  ],
  "abstract": "We present the classical theory of preservation of $\\sqsubset$-unbounded families in generic extensions by ccc posets, where $\\sqsubset$ is a definable relation of certain type on spaces of real numbers, typically associated with some classical cardinal invariant. We also prove that, under some conditions, these preservation properties can be preserved in direct limits of an iteration, so applications are extended beyond the context of finite support iterations. Also, we make a breve exposition of Shelah's theory of forcing with an ultrapower of a poset by a measurable cardinal.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-15T12:39:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E17",
      "03E35",
      "03E40"
    ],
    "keywords": [
      "preservation properties",
      "finite support iterations",
      "real numbers",
      "direct limits",
      "generic extensions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150103649A"
    }
  }
}