Two inequalities between cardinal invariants

by Raghavan and Shelah. [RaSh:1060]

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} ({Z}_0) <= {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 {s}_kappa <= {b}_kappa .

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