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 σ-compact subsets of the irrationals. It is consistent that all entries of Cichoń’s diagram are pairwise different (apart from add(M) and cof(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.