On cardinal characteristics associated with the strong measure zero ideal
Volume 257 / 2022
Fundamenta Mathematicae 257 (2022), 289-304
MSC: 03E10, 03E17, 03E35.
DOI: 10.4064/fm83-11-2021
Published online: 24 February 2022
Abstract
Let $\mathcal {SN}$ be the strong measure zero $\sigma $-ideal. We prove a result providing bounds for $\mathrm {cof}(\mathcal {SN})$, similar to Yorioka’s 2020 result on $\mathcal {SN}$. This is used to prove that $\mathrm {add}(\mathcal {SN})=\mathrm {cof}(\mathcal {SN}) \lt \mathrm {non}(\mathcal {SN}) \lt \mathrm {cof}(\mathcal {SN})$ is consistent with ZFC (via a matrix iteration forcing construction).
