On cardinal characteristics of Yorioka ideals

Abstract

Yorioka [J. Symbolic Logic 67(4):1373-1384, 2002] introduced a class of ideals (parametrized by reals) on the Cantor space to prove that the relation between the size of the continuum and the cofinality of the strong measure zero ideal on the real line cannot be decided in ZFC. We construct a matrix iteration of ccc posets to force that, for many ideals in that class, their associated cardinal invariants (i.e. additivity, covering, uniformity and cofinality) are pairwise different. In addition, we show that, consistently, the additivity and cofinality of Yorioka ideals does not coincide with the additivity and cofinality (respectively) of the ideal of Lebesgue measure zero subsets of the real line.

35 pages, 3 figures. Submitted

References in corpus (4)

• Rothberger gaps in fragmented ideals
• Matrix iterations with vertical support restrictions
• Cichoń's maximum
• The left side of Cichoń's diagram

Cited by in corpus (9)

• Filter-linkedness and its effect on preservation of cardinal characteristics
• Many Different Uniformity Numbers of Yorioka Ideals
• Controlling cardinal characteristics without adding reals
• More about the cofinality and the covering of the ideal of strong measure zero sets
• Uniformity numbers of the null-additive and meager-additive ideals
• Continuum Many Different Things: Localisation, Anti-Localisation and Yorioka Ideals
• Cardinal invariants associated with Hausdorff measures
• Cardinal Characteristics on Bounded Generalised Baire Spaces
• Directed schemes of ideals and cardinal characteristics, I: the meager additive ideal