📝 SummarXiv

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 $\mathfrak{s}_\rho$ and $\mathfrak{r}_\rho$ for $\rho\in (0,1)$, and show that $\mathfrak{r}_\rho$ does not depend on $\rho$.