Two inequalities between cardinal invariants
Tom 237 / 2017
Fundamenta Mathematicae 237 (2017), 187-200
MSC: 03E17, 03E55, 03E05, 03E20.
DOI: 10.4064/fm253-7-2016
Opublikowany online: 1 December 2016
Streszczenie
We prove two inequalities between cardinal invariants. The first inequality involves cardinal invariants associated with an analytic P-ideal, in particular the ideal of subsets of \omega of asymptotic density 0. We obtain an upper bound on the \ast -covering number, sometimes also called the weak covering number, of this ideal by proving that {\rm cov }^{\ast }({{\mathcal {Z}}}_{0}) \leq {\mathfrak {d}}. Next, we investigate the relationship between the bounding and splitting numbers at regular uncountable cardinals. We prove that, in sharp contrast to the case when \kappa = \omega , if \kappa is any regular uncountable cardinal, then {\mathfrak {s}}_{\kappa } \leq {\mathfrak {b} }_{\kappa }.
