Proceedings of the American Mathematical Society

Author(s): Shai Ben-David; Saharon Shelah
Journal: Proc. Amer. Math. Soc. 124 (1996), 2827-2837.
MSC (1991): Primary 03E35, 03E55, 04A20
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Abstract: 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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 03E35, 03E55, 04A20

Shai Ben-David
Affiliation: Department of Computer Science, Technion-Israel Institute of Technology, Haifa, Israel
Email: shai@cs.technion.ac.il

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