{
  "id": "2008.01225",
  "version": "v1",
  "published": "2020-08-03T22:22:31.000Z",
  "updated": "2020-08-03T22:22:31.000Z",
  "title": "An Inconsistent Forcing Axiom at $ω_2$",
  "authors": [
    "Stevo Todorčević",
    "Shihao Xiong"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We show that the forcing axiom for countably compact, $\\omega_2$-Knaster, well-met posets is inconsistent. This is supplemental to an inconsistency result of Shelah and sets a new limit to the generalization of Martin's Axiom to the stage of $\\omega_2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-03T22:22:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E57",
      "03E35",
      "03E05"
    ],
    "keywords": [
      "inconsistent forcing axiom",
      "well-met posets",
      "inconsistency result",
      "martins axiom",
      "countably compact"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}