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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DOI 10.2307/2586586
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Joel D. Hamkins (2009). Tall Cardinals. Mathematical Logic Quarterly 55 (1):68-86.
Joel David Hamkins (1998). Destruction or Preservation as You Like It. Annals of Pure and Applied Logic 91 (2-3):191-229.
Spencer Unger (2015). Fragility and Indestructibility II. Annals of Pure and Applied Logic 166 (11):1110-1122.

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