{
  "id": "1605.05489",
  "version": "v1",
  "published": "2016-05-18T09:20:20.000Z",
  "updated": "2016-05-18T09:20:20.000Z",
  "title": "Aronszajn trees, square principles, and stationary reflection",
  "authors": [
    "Chris Lambie-Hanson"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We investigate questions involving Aronszajn trees, square principles, and stationary reflection. We first consider two strengthenings of $\\square(\\kappa)$ introduced by Brodsky and Rinot for the purpose of constructing $\\kappa$-Souslin trees. Answering a question of Rinot, we prove that the weaker of these strengthenings is compatible with stationary reflection at $\\kappa$ but the stronger is not. We then prove that, if $\\mu$ is a singular cardinal, $\\square_\\mu$ implies the existence of a special $\\mu^+$-tree with a $\\mathrm{cf}(\\mu)$-ascent path, thus answering a question of L\\\"{u}cke. We show this result is sharp by proving that $\\square_{\\mu, 2}$ is compatible with the statement that every tree of height $\\mu^+$ with a narrow ascent path has a cofinal branch.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-18T09:20:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E35",
      "03E05",
      "03E55"
    ],
    "keywords": [
      "stationary reflection",
      "square principles",
      "aronszajn trees",
      "narrow ascent path",
      "souslin trees"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}