The two-cardinals transfer property and resurrection of supercompactness 󠀼span style=󠀢color:red󠀢󠀾This article has been retracted󠀼/span󠀾

Abstract

We show that the transfer property ( ℵ 1 , ℵ 0 ) → ( λ + , λ ) (\aleph _1,\aleph _0)\to (\lambda ^+,\lambda ) for singular λ \lambda does not imply (even) the existence of a non-reflecting stationary subset of λ + \lambda ^+ . The result assumes the consistency of ZFC with the existence of infinitely many supercompact cardinals. We employ a technique of “resurrection of supercompactness”. Our forcing extension 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 extension.