Instytut Matematyczny Polskiej Akademii Nauk / Institute of Mathematics / Publishing house / Journals and Serials / Fundamenta Mathematicae / All issues

Abstract

Let $\mathcal E$ denote the $\sigma $-ideal generated by closed null sets on the reals. We show that the uniformity and the covering of $\mathcal {E}$ can be added to Cichoń’s maximum with distinct values. More specifically, it is consistent that $\aleph _1 \lt \mathrm{add}(\mathcal {N}) \lt \mathrm{cov}(\mathcal N) \lt \mathfrak b \lt \mathrm{non}(\mathcal E) \lt \mathrm{non}(\mathcal M) \lt \mathrm{cov}(\mathcal {M}) \lt \mathrm{cov}(\mathcal {E}) \lt \mathfrak {d} \lt \mathrm {non}(\mathcal {N}) \lt \mathrm{cof}(\mathcal N) \lt 2^{\aleph _0}$ holds.