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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The two-cardinals transfer property
and resurrection of supercompactness


Authors: Shai Ben-David and Saharon Shelah
Journal: Proc. Amer. Math. Soc. 124 (1996), 2827-2837
MSC (1991): Primary 03E35, 03E55, 04A20
MathSciNet review: 1326996
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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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Additional Information

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

Saharon Shelah
Affiliation: Department of Mathematics, The Hebrew University, Jerusalem, Israel

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03327-8
PII: S 0002-9939(96)03327-8
Received by editor(s): December 14, 1989
Received by editor(s) in revised form: March 13, 1995
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1996 American Mathematical Society