# Sh:E91

• Ben-David, S., & Shelah, S. (1996). Retracted: The two-cardinals transfer property and resurrection of supercompactness. Proc. Amer. Math. Soc., 124(9), 2827–2837. NB: There is a flaw in the proof of the main theorem
• Abstract:
We show that the transfer property (\aleph_1,\aleph_0) \rightarrow(\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 inifinitely 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.
• published version (11p)
Bib entry
@article{Sh:E91,
author = {Ben-David, Shai and Shelah, Saharon},
title = {{Retracted: The two-cardinals transfer property and resurrection of supercompactness}},
journal = {Proc. Amer. Math. Soc.},
fjournal = {Proceedings of the American Mathematical Society},
volume = {124},
number = {9},
year = {1996},
pages = {2827--2837},
issn = {0002-9939},
mrnumber = {1326996},
mrclass = {03E05 (03E35 03E40)},
doi = {10.1090/S0002-9939-96-03327-8},
note = {NB: There is a flaw in the proof of the main theorem}
}