Small forcing makes any cardinal superdestructible

Journal of Symbolic Logic 63 (1):51-58 (1998)
Small forcing always ruins the indestructibility of an indestructible supercompact cardinal. In fact, after small forcing, any cardinal κ becomes superdestructible--any further <κ--closed forcing which adds a subset to κ will destroy the measurability, even the weak compactness, of κ. Nevertheless, after small forcing indestructible cardinals remain resurrectible, but never strongly resurrectible
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Joel D. Hamkins (2009). Tall Cardinals. Mathematical Logic Quarterly 55 (1):68-86.
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