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

TL;DR

This paper proves the consistency of certain inequalities between cardinal characteristics related to non-meager sets, irreducibility, and other set-theoretic properties, addressing open questions in the field.

Contribution

It establishes the consistency of several inequalities between cardinal invariants, resolving previously open questions in set theory.

Findings

Proves $rak{r}_{ ext{nwd}}<rak{irr}$ is consistent.

Shows $rak{r}_{ ext{nwd}}<rak{i}$ is consistent.

Establishes $rak{r}_{ ext{scatt}}<rak{irr}$ and $rak{r}_Q<rak{u}_Q$ are consistent.

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 $\mathfrak{r}_\mathbb{Q}<\mathfrak{u}_\mathbb{Q}$.