Con($\mathfrak{r}_{\mathsf{nwd}}<\mathfrak{irr}$)

Abstract

We prove the consistency of the inequality $\mathfrak{r}_{\mathsf{nwd}}<\mathfrak{irr}$, which in turn implies the consistency of $\mathfrak{r}_\mathsf{nwd}<\mathfrak{i}$ and $\mathfrak{r}_{\mathsf{scatt}}<\mathfrak{irr}$. This answers one question from \cite{balzar_hrusak_hernandez} and one question from \cite{cancino_irresolvable_1}. We also prove the consistency of the inequality $\mathfrak{r}_\mathbb{Q}<\mathfrak{u}_\mathbb{Q}$.