Cichoń's maximum without large cardinals
Summary: 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 \(\mathrm{add}(\mathcal{M})\) and \(\mathrm{cof}(\mathcal{M})\), 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.
scientific article; zbMATH DE number 7608245
scientific article