Mixed Levels of Indestructibility

Arthur W. Apter
2015 Bulletin of the Polish Academy of Sciences Mathematics  
Starting from a supercompact cardinal κ, we force and construct a model in which κ is both the least strongly compact and least supercompact cardinal and κ exhibits mixed levels of indestructibility. Specifically, κ's strong compactness, but not its supercompactness, is indestructible under any κ-directed closed forcing which also adds a Cohen subset of κ. On the other hand, in this model, κ's supercompactness is indestructible under any κ-directed closed forcing which doesn't add a Cohen
more » ... of κ. * 2010 Mathematics Subject Classifications: 03E35, 03E55. †
doi:10.4064/ba63-2-2 fatcat:x2hqit75hjdejhlfvtbulorg5m