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1 results

  • Cardinal invariants of monotone and porous sets

  • Michael Hrušák, Ondřej Zindulka
  • Journal:
    The Journal of Symbolic Logic / Volume 77 / Issue 1 / March 2012
    Published online by Cambridge University Press:
    12 March 2014, pp. 159-173
    Print publication:
    March 2012

  • A metric space (X, d) is monotone if there is a linear order < on X and a constant c such that d(x, y) ≤ c d(x, z) for all x < y < z in X. We investigate cardinal invariants of the σ-ideal Mon generated by monotone subsets of the plane. Since there is a strong connection between monotone sets in the plane and porous subsets of the line, plane and the Cantor set, cardinal invariants of these ideals are also investigated. In particular, we show that non(Mon) ≥ mσ-linked, but non(Mon) < mσ-centered is consistent. Also cov(Mon) < c and cof (N) < cov(Mon) are consistent.