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,
$\aleph _1 < \mathrm{add}(\mathcal {N})$ $\lt \mathrm{cov}(\mathcal {N}) < \mathfrak {b} < \mathrm{non}(\mathcal {M}) < \mathrm{cov}(\mathcal {M}) < \mathfrak{d} < \mathrm{non}(\mathcal{N}) < \mathrm{cof}(\mathcal{N}) < 2^{\aleph _0}$.