{
  "id": "1002.2192",
  "version": "v1",
  "published": "2010-02-10T20:00:10.000Z",
  "updated": "2010-02-10T20:00:10.000Z",
  "title": "More on cardinal invariants of analytic P-ideals",
  "authors": [
    "Barnabás Farkas",
    "Lajos Soukup"
  ],
  "journal": "Comment. Math. Univ. Carolin., 50(2009), 281-295",
  "categories": [
    "math.LO"
  ],
  "abstract": "Given an ideal $I$ on $\\omega$ let $a(I) $ ($\\bar{a}(I)$) be minimum of the cardinalities of infinite (uncountable) maximal $I$-almost disjoint subsets of $[{\\omega}]^{\\omega}$, and denote $b_I$ and$d_I$ the unbounding and dominating numbers of $(\\omega^\\omega,\\le_I)$. We show that (1) $a(I)>omega$ if $I$ is a summable ideal; (2) $a(Z)=\\omega$ and $\\bar{a}(Z)\\le a$ if $Z$ is a tall density ideal, (3) $b\\le \\bar{a}(I)$, and $b_I=b$ and $d_I=d$, for any analytic P-ideal $I$ on $\\omega$. Given an analytic $P$-ideal $I$ we investigate the relationship between the Sack, the $I$-bounding, $I$-dominating and ${\\omega}^{\\omega}$-bounding properties of a given poset $P$. For example, for the density zero ideal $Z$ we can prove: (i) a poset $P$ is $Z$-bounding iff it has the Sacks property, (ii) if $P$ adds a slalom capturing all ground model reals then $P$ is $Z$-dominating.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-02-10T20:00:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03E35",
      "03E17"
    ],
    "keywords": [
      "analytic p-ideal",
      "cardinal invariants",
      "tall density ideal",
      "density zero ideal",
      "ground model reals"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1002.2192F"
    }
  }
}