Cichoń's maximum

Abstract

Assuming four strongly compact cardinals, it is consistent that all entries in Cichoń's diagram (apart from $\mathrm{add}(\mathcal{M})$ and $\mathrm{cof}(\mathcal{M})$, whose values are determined by the others) are pairwise different; more specifically, $\aleph_1 \lt \mathrm{add}(\mathcal{N}) \lt \mathrm{cov}(\mathcal{N}) \lt \mathfrak{b} \lt \mathrm{non}(\mathcal{M}) \lt \mathrm{cov}(\mathcal{M})\lt \mathfrak{d} \lt \mathrm{non}(\mathcal{N}) \lt \mathrm{cof}(\mathcal{N}) \lt 2^{\aleph_0}$.