Cichoń's maximum with evasion number

Abstract

We show that the evasion number $\mathfrak{e}$ can be added to Cichoń's maximum with a distinct value. More specifically, it is consistent that ${\aleph }_1<\mathrm{add}(\mathcal{N})<\mathrm{cov}(\mathcal{N})<\mathfrak{b}<\mathfrak{e}<\mathrm{non}(\mathcal{M})<\mathrm{cov}(\mathcal{M})<\mathfrak{d}<\mathrm{non}(\mathcal{N})<\mathrm{cof}(\mathcal{N})<2^{{\aleph }_0}$ holds.

33pages,11figures