On Foreman's maximality principle
Logic
2016-04-05 v2
Abstract
In this paper we consider the Foreman's maximality principle, which says that any non-trivial forcing notion either adds a new real or collapses some cardinals. We prove the consistency of some of its consequences. We prove that it is consistent that every forcing adds a real and that for every uncountable regular cardinal , every -closed forcing of size collapses some cardinals.
Keywords
Cite
@article{arxiv.1502.07470,
title = {On Foreman's maximality principle},
author = {Mohammad Golshani and Yair Hayut},
journal= {arXiv preprint arXiv:1502.07470},
year = {2016}
}
Comments
The proof of Lemma 6.3 has changed, and the large cardinal assumption used in earlier version is reduced