Algebra Seminar talk
2024-11-29
Takashi Yamazoe
Cichoń's maximum with cardinals of the closed null ideal
Abstract:
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 $\aleph_1<\operatorname{add}(\mathcal{N})<\operatorname{cov}(\mathcal{N})<\mathfrak{b}<\operatorname{non}(\mathcal{E})<\operatorname{non}(\mathcal{M})<\operatorname{cov}(\mathcal{M})<\operatorname{cov}(\mathcal{E})<\mathfrak{d}<\operatorname{non}(\mathcal{N})<\operatorname{cof}(\mathcal{N})<2^{\aleph_0}$ holds. This talk is related to the speaker's previous talk at the Research Seminar in Set Theory at Uni Wien.