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

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

MathSciNet review:
1326996

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that the transfer property for singular does not imply (even) the existence of a non-reflecting stationary subset of . 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:
https://doi.org/10.1090/S0002-9939-96-03327-8

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