{
  "id": "1409.8335",
  "version": "v1",
  "published": "2014-09-29T21:50:45.000Z",
  "updated": "2014-09-29T21:50:45.000Z",
  "title": "A note on a new ideal",
  "authors": [
    "Adam Kwela"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper we study a new ideal $\\mathcal{WR}$. The main result is the following: an ideal is not weakly Ramsey if and only if it is above $\\mathcal{WR}$ in the Kat\\v{e}tov order. Weak Ramseyness was introduced by Laflamme in order to characterize winning strategies in a certain game. We apply result of Natkaniec and Szuca to conclude that $\\mathcal{WR}$ is critical for ideal convergence of sequences of quasi-continuous functions. We study further combinatorial properties of $\\mathcal{WR}$ and weak Ramseyness. Answering a question of Filip\\'ow et al. we show that $\\mathcal{WR}$ is not $2$-Ramsey, but every ideal on $\\omega$ isomorphic to $\\mathcal{WR}$ is Mon (every sequence of reals contains a monotone subsequence indexed by a $\\mathcal{I}$-positive set).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-29T21:50:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E05"
    ],
    "keywords": [
      "weak ramseyness",
      "main result",
      "ideal convergence",
      "combinatorial properties",
      "reals contains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1409.8335K"
    }
  }
}