# Sh:1060

• Raghavan, D., & Shelah, S. (2017). Two inequalities between cardinal invariants. Fund. Math., 237(2), 187–200.
• Abstract:
We prove two ZFC 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 aymptotic density 0. We obtain an upper bound on the \ast-covering number, sometimes also called the weak covering number, of this ideal by proving in Section 2 that cov{\ast} (\mathcal{Z}_0) \leq \mathfrak{d}.

In Section 3 we investigate the relationship between the bounding and splitting numbers at regular uncountable cardinals. We prove in sharp contrast to the case when \kappa = \omega, that if \kappa is any regular uncountable cardinal, then \mathfrak{s}_\kappa \leq \mathfrak{b}_\kappa.

• published version (14p)
Bib entry
@article{Sh:1060,
author = {Raghavan, Dilip and Shelah, Saharon},
title = {{Two inequalities between cardinal invariants}},
journal = {Fund. Math.},
fjournal = {Fundamenta Mathematicae},
volume = {237},
number = {2},
year = {2017},
pages = {187--200},
issn = {0016-2736},
mrnumber = {3615051},
mrclass = {03E17 (03E05 03E20 03E55)},
doi = {10.4064/fm253-7-2016},
note = {\href{https://arxiv.org/abs/1505.06296}{arXiv: 1505.06296}},
arxiv_number = {1505.06296}
}