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2 results

  • THE COVERING NUMBERS OF SOME MYCIELSKI IDEALS MAY BE DIFFERENT

  • Part of
  • OTMAR SPINAS
  • Journal:
    The Journal of Symbolic Logic / Volume 90 / Issue 1 / March 2025
    Published online by Cambridge University Press:
    30 January 2025, pp. 252-277
    Print publication:
    March 2025
    • Article
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      • Open access
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  • We show that in the Silver model the inequality $\mathrm {cov}(\mathfrak {C} _2) < \mathrm {cov}(\mathfrak {P}_2)$ holds true, where $\mathfrak {C}_2$ and $\mathfrak {P}_2$ are the two-dimensional Mycielski ideals.

  • SILVER ANTICHAINS

  • OTMAR SPINAS, MAREK WYSZKOWSKI
  • Journal:
    The Journal of Symbolic Logic / Volume 80 / Issue 2 / June 2015
    Published online by Cambridge University Press:
    22 April 2015, pp. 503-519
    Print publication:
    June 2015

  • In this paper we investigate the structure of uncountable maximal antichains of Silver forcing and show that they have to be at least of size d, where d is the dominating number. Part of this work can be used to show that the additivity of the Silver forcing ideal has size at least the unbounding number b. It follows that every reasonable amoeba Silver forcing adds a dominating real.