Cicho\'n'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 Cicho\'n's diagram are pairwise different (apart from $\textrm{ add}(\mathcal{ M})$ and $\textrm{ cof}(\mathcal{ M})$, 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.
Categories: math.LO