{
  "id": "math/9902054",
  "version": "v1",
  "published": "1999-02-08T16:01:49.000Z",
  "updated": "1999-02-08T16:01:49.000Z",
  "title": "Antichains in products of linear orders",
  "authors": [
    "Martin Goldstern",
    "Saharon Shelah"
  ],
  "comment": "9 pages",
  "categories": [
    "math.LO",
    "math.GN"
  ],
  "abstract": "1. For many regular cardinals lambda (in particular, for all successors of singular strong limit cardinals, and for all successors of singular omega-limits), for all n in {2,3,4, ...} : There is a linear order L such that L^n has no (incomparability-)antichain of cardinality lambda, while L^{n+1} has an antichain of cardinality lambda . 2. For any nondecreasing sequence (lambda2,lambda3, ...) of infinite cardinals it is consistent that there is a linear order L such that L^n has an antichain of cardinality lambda_n, but not one of cardinality lambda_n^+ .",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-02-08T16:01:49.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E35",
      "03E04",
      "06A05"
    ],
    "keywords": [
      "linear order",
      "singular strong limit cardinals",
      "cardinality lambda",
      "regular cardinals lambda",
      "singular omega-limits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......2054G"
    }
  }
}