Cichoń's maximum

Abstract

Assuming four strongly compact cardinals, it is consistent that all entries in Cichoń's diagram are pairwise different, more specifically that \[ \aleph_1 < \mathrm{add}(\mathrm{null}) < \mathrm{cov}(\mathrm{null}) < \mathfrak{b} < \mathrm{non}(\mathrm{meager}) < \mathrm{cov}(\mathrm{meager}) < \mathfrak{d} < \mathrm{non}(\mathrm{null}) < \mathrm{cof}(\mathrm{null}) < 2^{\aleph_0}.\]

Minor corrections. Section 2 expanded and split into two sections: Now we do not directly apply Boolean ultrapowers to the forcing anymore, but first define the embedding from the Boolean ultrapower and then only work with the embedding. This paper now supersedes arXiv:1706.09638