{
  "id": "math/9505212",
  "version": "v1",
  "published": "1995-05-15T00:00:00.000Z",
  "updated": "1995-05-15T00:00:00.000Z",
  "title": "A game on partial orderings",
  "authors": [
    "Sakaé Fuchino",
    "Sabine Koppelberg",
    "Saharon Shelah"
  ],
  "journal": "Topology Appl. 74 (1996), 141-148",
  "categories": [
    "math.LO"
  ],
  "abstract": "We study the determinacy of the game G_kappa (A) introduced in [FKSh:549] for uncountable regular kappa and several classes of partial orderings A. Among trees or Boolean algebras, we can always find an A such that G_kappa (A) is undetermined. For the class of linear orders, the existence of such A depends on the size of kappa^{< kappa}. In particular we obtain a characterization of kappa^{< kappa}= kappa in terms of determinacy of the game G_kappa (L) for linear orders L .",
  "revisions": [
    {
      "version": "v1",
      "updated": "1995-05-15T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "partial orderings",
      "linear orders",
      "uncountable regular kappa",
      "boolean algebras",
      "determinacy"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1995math......5212F"
    }
  }
}