{
  "id": "2304.02132",
  "version": "v1",
  "published": "2023-04-04T21:34:44.000Z",
  "updated": "2023-04-04T21:34:44.000Z",
  "title": "Narrow systems revisited",
  "authors": [
    "Chris Lambie-Hanson"
  ],
  "comment": "18 pages",
  "categories": [
    "math.LO"
  ],
  "abstract": "Motivated by two open questions about two-cardinal tree properties, we introduce and study generalized narrow system properties. The first of these questions asks whether the strong tree property at a regular cardinal $\\kappa \\geq \\omega_2$ implies the Singular Cardinals Hypothesis ($\\mathsf{SCH}$) above $\\kappa$. We show here that a certain narrow system property at $\\kappa$ that is closely related to the strong tree property, and holds in all known models thereof, suffices to imply $\\mathsf{SCH}$ above $\\kappa$. The second of these questions asks whether the strong tree property can consistenty hold simultaneously at all regular cardinals $\\kappa \\geq \\omega_2$. We show here that the analogous question about the generalized narrow system property has a positive answer. We also highlight some connections between generalized narrow system properties and the existence of certain strongly unbounded subadditive colorings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-04T21:34:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E05",
      "03E35",
      "03E55",
      "03E04"
    ],
    "keywords": [
      "generalized narrow system property",
      "strong tree property",
      "regular cardinal",
      "study generalized narrow system properties",
      "questions asks"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}