Small forcing creates neither strong nor Woodin cardinals
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- by Joel David Hamkins and W. Hugh Woodin PDF
- Proc. Amer. Math. Soc. 128 (2000), 3025-3029 Request permission
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
- A. Lévy and R. M. Solovay, Measurable cardinals and the continuum hypothesis, Israel J. Math. 5 (1967), 234–248. MR 224458, DOI 10.1007/BF02771612
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
- MR Author ID: 347679
- Email: jhamkins@gc.cuny.edu
- W. Hugh Woodin
- Affiliation: Department of Mathematics, University of California, Berkeley, California 94720
- Email: woodin@math.berkeley.edu
- 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.
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 128 (2000), 3025-3029
- MSC (1991): Primary 03E55, 03E40
- DOI: https://doi.org/10.1090/S0002-9939-00-05347-8
- MathSciNet review: 1664390