{
  "id": "1310.4042",
  "version": "v2",
  "published": "2013-10-15T12:56:28.000Z",
  "updated": "2020-07-29T15:08:44.000Z",
  "title": "Forcing axioms for $λ$-complete $μ^+$-C.C",
  "authors": [
    "Saharon Shelah"
  ],
  "comment": "revised version (after referee's comments)",
  "categories": [
    "math.LO"
  ],
  "abstract": "We note that some form of the condition \"$p_1, p_2$ have a $\\leq_{\\mathbb{Q}}$-lub in $\\mathbb{Q}$\" is necessary in some forcing axiom for $\\lambda$-complete $\\mu^+$-c.c. forcing notions. We also show some versions are really stronger than others.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-10-15T12:56:28.000Z",
      "abstract": "We note that some form of the condition \"p_1, p_2 have a >_Q-lub in Q\" is necessary in some forcing axiom for lambda-complete mu^+-c.c. forcing notions. We also show some versions are really stronger than others, a strong way to answer Alexie's question of having P satisfying one condition but no P' equivalent to P satisfying another. We have not looked systematically whether any such question (of interest) is open.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2020-07-29T15:08:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E35",
      "03E05"
    ],
    "keywords": [
      "forcing axiom",
      "answer alexies question",
      "strong way",
      "really stronger",
      "lambda-complete"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1310.4042S"
    }
  }
}