Small Forcing Makes Any Cardinal Superdestructible
Logic
2016-07-05 v1
Abstract
Small forcing always ruins the indestructibility of an indestructible supercompact cardinal. In fact, after small forcing, any cardinal becomes superdestructible---any further -closed forcing which adds a subset to will destroy the measurability, even the weak compactness, of . Nevertheless, after small forcing indestructible cardinals remain resurrectible, but never strongly resurrectible.
Cite
@article{arxiv.1607.00684,
title = {Small Forcing Makes Any Cardinal Superdestructible},
author = {Joel David Hamkins},
journal= {arXiv preprint arXiv:1607.00684},
year = {2016}
}
Comments
This paper appeared in 1998; I have finally now uploaded the article to the arxiv. Commentary concerning this article can be made on the author's blog at http://jdh.hamkins.org/superdestructibility/