Cichoń’s maximum without large cardinals

Abstract

Cichoń’s diagram lists twelve cardinal characteristics (and the provable inequalities between them) associated with the ideals of null sets, meager sets, countable sets, and $\sigma$-compact subsets of the irrationals. It is consistent that all entries of Cichoń’s diagram are pairwise different (apart from $\operatorname{add}\mathcal{M}$ and $\operatorname{cof}\mathcal{M}$, which are provably equal to other entries). However, the consistency proofs so far required large cardinal assumptions. In this work, we show the consistency without such assumptions.