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

 

Small forcing creates neither strong nor Woodin cardinals


Authors: Joel David Hamkins and W. Hugh Woodin
Journal: Proc. Amer. Math. Soc. 128 (2000), 3025-3029
MSC (1991): Primary 03E55, 03E40
Published electronically: April 28, 2000
MathSciNet review: 1664390
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Abstract: After small forcing, almost every strongness embedding is the lift of a strongness embedding in the ground model. Consequently, small forcing creates neither strong nor Woodin cardinals.


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Additional Information

Joel David Hamkins
Affiliation: Mathematics Program, The Graduate Center of the City University of New York, 365 Fifth Avenue, New York, New York 10016
Email: jhamkins@gc.cuny.edu

W. Hugh Woodin
Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
Email: woodin@math.berkeley.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05347-8
PII: S 0002-9939(00)05347-8
Keywords: Small forcing, large cardinals, strong cardinal, Woodin cardinal.
Received by editor(s): September 1, 1998
Received by editor(s) in revised form: November 9, 1998
Published electronically: April 28, 2000
Additional Notes: The research of the first author has been supported in part by grants from the PSC-CUNY Research Foundation, and of the second author, by grants from the NSF
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 2000 American Mathematical Society