TY - JOUR
T1 - The two-cardinals transfer property and resurrection of supercompactness
AU - Ben-David, Shai
AU - Shelah, Saharon
PY - 1996
Y1 - 1996
N2 - We show that the transfer property (N1, N0) → (λ+, λ) for singular λ does not imply (even) the existence of a non-reflecting stationary subset of λ+ 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.
AB - We show that the transfer property (N1, N0) → (λ+, λ) for singular λ does not imply (even) the existence of a non-reflecting stationary subset of λ+ 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.
UR - http://www.scopus.com/inward/record.url?scp=33645906550&partnerID=8YFLogxK
U2 - 10.1090/s0002-9939-96-03327-8
DO - 10.1090/s0002-9939-96-03327-8
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AN - SCOPUS:33645906550
SN - 0002-9939
VL - 124
SP - 2827
EP - 2837
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 9
ER -