{
  "id": "2208.14896",
  "version": "v1",
  "published": "2022-08-31T14:41:08.000Z",
  "updated": "2022-08-31T14:41:08.000Z",
  "title": "MA$_{ω_1}(S)[S]$ does not imply $\\mathcal{K}_2$",
  "authors": [
    "Yinhe Peng",
    "Liuzhen Wu"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We construct a model in which MA$_{\\omega_1}$(S)[S] holds and $\\mathcal{K}_2$ fails. This shows that MA$_{\\omega_1}$(S)[S] does not imply $\\mathcal{K}_2$ and answers an old question of Larson and Todorcevic in [3]. We also investigate different strong colorings in models of MA$_{\\omega_1}$(S)[S].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-31T14:41:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E02",
      "03E35",
      "03E65"
    ],
    "keywords": [
      "old question",
      "strong colorings",
      "todorcevic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}