September 27
Takashi Yamazoe,
Kobe University
Cichoń's maximum with the uniformity and the covering of the $\sigma$-ideal $\mathcal{E}$ generated by closed null sets
Let $\mathcal{E}$ denote the $\sigma$-ideal generated by closed null sets on $\mathbb{R}$. 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 $\aleph_1\lt\mathrm{add}(\mathcal{N})\lt\mathrm{cov}(\mathcal{N})\lt\mathfrak{b}\lt\mathrm{non}(\mathcal{E})\lt\mathrm{non}(\mathcal{M})\lt\mathrm{cov}(\mathcal{M})\lt\mathrm{cov}(\mathcal{E})\lt\mathfrak{d}\lt\mathrm{non}(\mathcal{N})\lt\mathrm{cof}(\mathcal{N})\lt2^{\aleph_0}$ holds.