{
  "id": "math/9302203",
  "version": "v1",
  "published": "1993-02-26T00:00:00.000Z",
  "updated": "1993-02-26T00:00:00.000Z",
  "title": "Combinatorics on Ideals and Axiom A",
  "authors": [
    "James Sharp"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "Throughout this abstract let U be a fixed p-point ultrafilter and let I be the dual ideal. Grigorieff forcing is P(U)={p:omega to 2|dom(p) is an element of I} ordered by reverse inclusion. It is well known that Grigorieff forcing is proper. The main result of this paper is the following: THEOREM: Gregorieff forcing does not satisfy Axiom A. To prove this we use the following game, denoted G(U), for two players playing alternatively: Player I plays a partition of omega, {J_n| n<omega}, such that for all n<omega, J_n is an element of I; At the nth turn Player II plays a finite subset F_n of J_n. Player II wins iff the union of the F_n is an element of U. The following two Lemmas prove the Theorem: LEMMA 1: If P(U) satisfies axiom A, then player II has a winning strategy in the game G(U). LEMMA 2:The game G(U) is undetermined.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1993-02-26T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "combinatorics",
      "nth turn player",
      "reverse inclusion",
      "main result",
      "dual ideal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1993math......2203S"
    }
  }
}