Indestructibility and the level-by-level agreement between strong compactness and supercompactness
Logic
2007-05-23 v1
Abstract
Can a supercompact cardinal kappa be Laver indestructible when there is a level-by-level agreement between strong compactness and supercompactness? In this article, we show that if there is a sufficiently large cardinal above kappa, then no, it cannot. Conversely, if one weakens the requirement either by demanding less indestructibility, such as requiring only indestructibility by stratified posets, or less level-by-level agreement, such as requiring it only on measure one sets, then yes, it can.
Cite
@article{arxiv.math/0102086,
title = {Indestructibility and the level-by-level agreement between strong compactness and supercompactness},
author = {Arthur W. Apter and Joel David Hamkins},
journal= {arXiv preprint arXiv:math/0102086},
year = {2007}
}
Comments
22 pages