{
  "id": "2001.07977",
  "version": "v1",
  "published": "2020-01-22T12:11:08.000Z",
  "updated": "2020-01-22T12:11:08.000Z",
  "title": "Forcing Axioms, the Uniformization and the Basis Property",
  "authors": [
    "Stefan Hoffelner"
  ],
  "comment": "17 Pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "We show that there are models of MA where the boldface $\\Sigma^1_3$-uniformization property holds. Further we show that BPFA and the assertion $\\aleph_1$ is accessible to reals outright implies that the boldface $\\Sigma^1_3$-uniformization property is true. Further we show that MA and the $\\Pi^1_3$-basis property is consistent and that BPFA and $\\aleph_1$ is accessible to reals outright implies that the $\\Pi^1_3$-basis property is true.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-22T12:11:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E15",
      "03E35",
      "03E45",
      "03E57"
    ],
    "keywords": [
      "basis property",
      "forcing axioms",
      "reals outright implies",
      "uniformization property holds",
      "consistent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}