CARDINAL INVARIANTS RELATED TO DENSITY

Abstract

Abstract We investigate some variants of the splitting, reaping, and independence numbers defined using asymptotic density. Specifically, we give a proof of Con( $\mathfrak {i}<\mathfrak {s}_{1/2}$ ), Con( $\mathfrak {r}_{1/2}<\mathfrak {b}$ ), and Con( $\mathfrak {i}_*<2^{\aleph _0}$ ). This answers two questions raised in [5]. Besides, we prove the consistency of $\mathfrak {s}_{1/2}^{\infty } < $ non $(\mathcal {E})$ and cov $(\mathcal {E}) < \mathfrak {r}_{1/2}^{\infty }$ , where $\mathcal {E}$ is the $\sigma $ -ideal generated by closed sets of measure zero.