Indestructibility and the level-by-level agreement between strong compactness and supercompactness

Details Indestructibility and the level-by-level agreement between strong compactness and supercompactness Indestructibility and the level-by-level agreement between strong compactness and supercompactness

2001-02-10

arxiv.org/abs/math/0102086v1

Mathematics

Logic

22 pages

Scientific paper

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.

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