Cardinal invariants on universally null sets

Abstract

We investigate the cardinal invariants on universally null sets. In particular, we prove $\mathfrak{b} < \operatorname{cof}(\mathcal{UN})$ and $\operatorname{non}(\mathcal{N}) = \operatorname{non}(\mathcal{UN}) < \operatorname{cof}(\mathcal{UN})$ in $\mathsf{ZFC}$. Also, assuming $\operatorname{add}(\mathcal{N}) = \mathfrak{c}$, we prove $\operatorname{cof}(\mathcal{UN}) = \mathfrak{d}_\mathfrak{c}$ by adapting Yorioka&#39;s technique. Moreover, we prove the consistency of $\operatorname{add}(\mathcal{UN}) < \operatorname{cov}(\mathcal{UN}) < \operatorname{non}(\mathcal{UN}) < \operatorname{cof}(\mathcal{UN})$.