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Small forcing creates neither strong nor Woodin cardinals

Author(s): Joel David Hamkins; W. Hugh Woodin
Journal: Proc. Amer. Math. Soc. 128 (2000), 3025-3029.
MSC (1991): Primary 03E55, 03E40
Posted: April 28, 2000
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Abstract | References | Similar articles | Additional information

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.

References:

[LevSol67]: Azriel Levy, Robert M. Solovay, Measurable cardinals and the Continuum Hypothesis, IJM 5 (1967), 234-248. MR 37:57

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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: 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
Posted: 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.
Copyright of article: Copyright 2000, American Mathematical Society


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