# Sh:1060

- Raghavan, D., & Shelah, S. (2017).
*Two inequalities between cardinal invariants*. Fund. Math.,**237**(2), 187–200. arXiv: 1505.06296 DOI: 10.4064/fm253-7-2016 MR: 3615051 -
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} }