Indestructible weakly compact cardinals and the necessity of supercompactness for certain proof schemata
Logic
2007-05-23 v1
Abstract
We show that if the weak compactness of a cardinal is made indestructible by means of any preparatory forcing of a certain general type, including any forcing naively resembling the Laver preparation, then the cardinal was originally supercompact. We then apply this theorem to show that the hypothesis of supercompactness is necessary for certain proof schemata.
Keywords
Cite
@article{arxiv.math/9907046,
title = {Indestructible weakly compact cardinals and the necessity of supercompactness for certain proof schemata},
author = {Arthur W. Apter and Joel David Hamkins},
journal= {arXiv preprint arXiv:math/9907046},
year = {2007}
}
Comments
13 pages