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TL;DR

This paper proves the consistency of certain inequalities between cardinal invariants at a singular cardinal, advancing understanding in set theory and cardinal characteristics.

Contribution

It establishes the consistency of inequalities involving $rak{r}_lambda$, $rak{d}_lambda$, and $rak{u}_lambda$ at a singular cardinal, which was previously unknown.

Findings

Proves $rak{r}_lambda<rak{d}_lambda$ is consistent.

Proves $rak{u}_lambda<rak{d}_lambda$ is consistent.

Advances the theory of cardinal invariants at singular cardinals.

Abstract

We prove the consistency of $\mathfrak{r}_\lambda<\mathfrak{d}_\lambda$ and even $\mathfrak{u}_\lambda<\mathfrak{d}_\lambda$ for a singular cardinal $\lambda$.