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Fragile measurability

Published online by Cambridge University Press:  12 March 2014

Joel Hamkins
Joel Hamkins*
Affiliation:
Department of Mathematics, University of California, Berkeley, Berkeley, CA 94720, E-mail: HAMKINS@MATH.BERKELEY.EDU
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Abstract

Laver [L] and others [G-S] have shown how to make the supercompactness or strongness of κ indestructible by a wide class of forcing notions. We show, alternatively, how to make these properties fragile. Specifically, we prove that it is relatively consistent that any forcing which preserves κ<κ and κ+, but not P(κ), destroys the measurability of κ, even if κ is initially supercompact, strong, or if I1(κ) holds. Obtained as an application of some general lifting theorems, this result is an “inner model” type of theorem proved instead by forcing.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 59 , Issue 1 , March 1994 , pp. 262 - 282
Copyright
Copyright © Association for Symbolic Logic 1994

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References

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