{
  "id": "2309.01931",
  "version": "v1",
  "published": "2023-09-05T03:37:25.000Z",
  "updated": "2023-09-05T03:37:25.000Z",
  "title": "Separating cardinal characteristics of the strong measure zero ideal",
  "authors": [
    "Jörg Brendle",
    "Miguel A. Cardona",
    "Diego A. Mejía"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "Let $\\mathcal{SN}$ be the $\\sigma$-ideal of the strong measure zero sets of reals. We present general properties of forcing notions that allow to control of the additivity of $\\mathcal{SN}$ after finite support iterations. This is applied to force that the four cardinal characteristics associated with $\\mathcal{SN}$ are pairwise different: \\[\\mathrm{add}(\\mathcal{SN})<\\mathrm{cov}(\\mathcal{SN})<\\mathrm{non}(\\mathcal{SN})<\\mathrm{cof}(\\mathcal{SN}).\\] Furthermore, we construct a forcing extension satisfying the above and Cicho\\'n's maximum (i.e. that the non-dependent values in Cicho\\'n's diagram are pairwise different).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-05T03:37:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E17",
      "03E35",
      "03E40"
    ],
    "keywords": [
      "strong measure zero ideal",
      "separating cardinal characteristics",
      "strong measure zero sets",
      "finite support iterations",
      "general properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}