{
  "id": "math/9804153",
  "version": "v1",
  "published": "1998-04-15T00:00:00.000Z",
  "updated": "1998-04-15T00:00:00.000Z",
  "title": "Sticks and clubs",
  "authors": [
    "Sakaé Fuchino",
    "Saharon Shelah",
    "Lajos Soukup"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We study combinatorial principles known as stick and club. Several variants of these principles and cardinal invariants connected to them are also considered. We introduce a new kind of side-by-side product of partial orders which we call pseudo-product. Using such products, we give several generic extensions where some of these principles hold together with not CH and Martin's Axiom for countable p.o.-sets. An iterative version of the pseudo-product is used under an inaccessible cardinal to show the consistency of the club principle for every stationary subset of limits of omega_1 together with not CH and Martin's Axiom for countable p.o.-sets.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-04-15T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "martins axiom",
      "study combinatorial principles",
      "cardinal invariants",
      "side-by-side product",
      "partial orders"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math......4153F"
    }
  }
}