English

Cardinal invariants on universally null sets

Logic 2026-07-14 v1

Abstract

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

Cite

@article{arxiv.2607.12936,
  title  = {Cardinal invariants on universally null sets},
  author = {Tatsuya Goto},
  journal= {arXiv preprint arXiv:2607.12936},
  year   = {2026}
}