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Published online by Cambridge University Press:  12 March 2014

M. C. Stanley
M. C. Stanley*
Affiliation:
Department of Mathematics, San Jose State University, San Jose, California 95192, E-mail: [email protected]
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Abstract

It is proved (Theorem 1) that if 0# exists, then any constructible forcing property which over L adds no reals, over V collapses an uncountable L-cardinal to cardinality ω. This improves a theorem of Foreman, Magidor, and Shelah. Also, a method for approximating this phenomenon generically is found (Theorem 2). The strategy is first to reduce the problem of ‘disabling’ forcing properties to that of specializing certain trees in a weak sense.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 57 , Issue 4 , December 1992 , pp. 1153 - 1175
Copyright
Copyright © Association for Symbolic Logic 1992

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References

[D]Dodd, A. J., The core model, London Mathematical Society Lecture Note Series, vol. 61, Cambridge University Press, Cambridge, 1982.CrossRefGoogle Scholar
[FMS]Foreman, M., Magidor, M., and Shelah, S., 0# and some forcing principles, this Journal, vol. 51 (1986), pp. 39–46.Google Scholar