More on Halfway New Cardinal Characteristics

Abstract

We continue investigating variants of the splitting and reaping numbers introduced in arXiv:1808.02442. In particular, answering a question raised there, we prove the consistency of $\mathrm{cof}(\mathcal{M})<{\mathfrak{s}}_{\frac{1}{2}}$ and of ${\mathfrak{r}}_{\frac{1}{2}}<\mathrm{add}(\mathcal{M})$. Moreover, we discuss their natural generalisations ${\mathfrak{s}}_{\ddot{I}}$ and ${\mathfrak{r}}_{\ddot{I}}$ for $\ddot{I}\in (0,1)$, and show that ${\mathfrak{r}}_{\ddot{I}}$ does not depend on $\ddot{I}$.

14 pages, 2 figures