{
  "id": "2308.12136",
  "version": "v1",
  "published": "2023-08-23T13:50:07.000Z",
  "updated": "2023-08-23T13:50:07.000Z",
  "title": "Game-theoretic variants of cardinal invariants",
  "authors": [
    "Jorge Antonio Cruz Chapital",
    "Tatsuya Goto",
    "Yusuke Hayashi"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "We investigate game-theoretic variants of cardinal invariants of the continuum. The invariants we treat are the splitting number $\\mathfrak{s}$, the reaping number $\\mathfrak{r}$, the bounding number $\\mathfrak{b}$, the dominating number $\\mathfrak{d}$ and the additivity number of the null ideal $\\operatorname{add}(\\mathsf{null})$. We also consider games, called tallness games, defined according to ideals on $\\omega$ and characterize that each of Player I and Player II has a winning strategy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-23T13:50:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "game-theoretic variants",
      "cardinal invariants",
      "additivity number",
      "null ideal",
      "tallness games"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}