Cicho\'n's maximum without large cardinals
Abstract
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 -compact subsets of the irrationals. It is consistent that all entries of Cicho\'n's diagram are pairwise different (apart from and , 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.
Keywords
Cite
@article{arxiv.1906.06608,
title = {Cicho\'n's maximum without large cardinals},
author = {Martin Goldstern and Jakob Kellner and Diego A. Mejía and Saharon Shelah},
journal= {arXiv preprint arXiv:1906.06608},
year = {2020}
}
Comments
Minor corrections. Remove "logical dependency" on arxiv:1904.02617 (Everything claimed about $\aleph_1<\mathfrak m<\mathfrak p<\mathfrak h<\textrm{add}(\mathcal{N})$ in the previous version is correct, but it is better proved in arxiv:1904.02617, bulding on this paper, than the other way round.)