English

Cicho\'n's maximum

Logic 2019-07-08 v3

Abstract

Assuming four strongly compact cardinals, it is consistent that all entries in Cicho\'n's diagram are pairwise different, more specifically that 1<add(null)<cov(null)<b<non(meager)<cov(meager)<d<non(null)<cof(null)<20. \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}.

Cite

@article{arxiv.1708.03691,
  title  = {Cicho\'n's maximum},
  author = {Martin Goldstern and Jakob Kellner and Saharon Shelah},
  journal= {arXiv preprint arXiv:1708.03691},
  year   = {2019}
}

Comments

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

R2 v1 2026-06-22T21:12:54.868Z