{
  "id": "math/0210162",
  "version": "v1",
  "published": "2002-10-10T19:37:06.000Z",
  "updated": "2002-10-10T19:37:06.000Z",
  "title": "On iterated forcing at successors of regular cardinals",
  "authors": [
    "Todd Eisworth"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We investigate the problem of when $\\leq\\lambda$--support iterations of $<\\lambda$--complete notions of forcing preserve $\\lambda^+$. We isolate a property -- {\\em properness over diamonds} -- that implies $\\lambda^+$ is preserved and show that this property is preserved by $\\lambda$--support iterations. We close with an application of our technology by presenting a consistency result on uniformizing colorings of ladder systems on $\\{\\delta<\\lambda^+:\\cf(\\delta)=\\lambda\\}$ that complements a theorem of Shelah.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-10-10T19:37:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "regular cardinals",
      "iterated forcing",
      "successors",
      "support iterations",
      "consistency result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math.....10162E"
    }
  }
}