English

On cardinal characteristics associated with the strong measure zero ideal

Logic 2020-03-19 v2

Abstract

Let SN\mathcal{SN} be the strong measure zero σ\sigma-ideal. We prove a result providing bounds for cof(SN)\mathrm{cof}(\mathcal{SN}) which implies Yorioka's characterization of the cofinality of the strong measure zero. In addition, we use forcing matrix iterations to construct a model of ZFC that satisfies add(SN)=cov(SN)<non(SN)<cof(SN)\mathrm{add}(\mathcal{SN})=\mathrm{cov}(\mathcal{SN})<\mathrm{non}(\mathcal{SN})<\mathrm{cof}(\mathcal{SN}).

Cite

@article{arxiv.2003.07066,
  title  = {On cardinal characteristics associated with the strong measure zero ideal},
  author = {Miguel A. Cardona},
  journal= {arXiv preprint arXiv:2003.07066},
  year   = {2020}
}
R2 v1 2026-06-23T14:15:49.624Z