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two-cardinals transfer property and resurrection of supercompactness 󠀼span style=󠀢color:red󠀢󠀾\textbf{This article has been retracted}󠀼/span󠀾

Ben-David, Shai; Shelah, Saharon

doi:10.1090/S0002-9939-96-03327-8

The two-cardinals transfer property and resurrection of supercompactness This article has been retracted
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by Shai Ben-David and Saharon Shelah

Proc. Amer. Math. Soc. 124 (1996), 2827-2837

DOI: https://doi.org/10.1090/S0002-9939-96-03327-8

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Abstract:

This article has been retracted. We show that the transfer property $(\aleph _1,\aleph _0)\to (\lambda ^+,\lambda )$ for singular $\lambda$ 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 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.

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