|Title:||The Two-Cardinals Transfer Property and Resurrection of Supercompactness
|Authors:||S. Ben-David and S. Shelah
|Abstract:||We show that the transfer property <Alef1,Alef0> to <Lambda+,Lambda> for singular A, does not imply (even) the existence of a non-reflecting stationary subset of Lambda+. The result assumes the consistency of ZFC with the existence of inifinitely many super compact cardinals. We employ a technique of "resurrection of supercompactness". Our forcing extention destroys the supercompactness of some cardinals, to show that in the extended model they still carry some of their compactness properties (such as reflection of stationary sets), we show that their supercompactness can be resurrected via a tame forcing extention.|
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