Small Forcing Makes any Cardinal Superdestructible
Hamkins, Joel David
J. Symbolic Logic, Tome 63 (1998) no. 1, p. 51-58 / Harvested from Project Euclid
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Small forcing always ruins the indestructibility of an indestructible supercompact cardinal. In fact, after small forcing, any cardinal $\kappa$ becomes superdestructible--any further <$\kappa$--closed forcing which adds a subset to $\kappa$ will destroy the measurability, even the weak compactness, of $\kappa$. Nevertheless, after small forcing indestructible cardinals remain resurrectible, but never strongly resurrectible.
Publié le : 1998-03-14
Classification:  
@article{1183745456,
     author = {Hamkins, Joel David},
     title = {Small Forcing Makes any Cardinal Superdestructible},
     journal = {J. Symbolic Logic},
     volume = {63},
     number = {1},
     year = {1998},
     pages = { 51-58},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183745456}
}

Hamkins, Joel David. Small Forcing Makes any Cardinal Superdestructible. J. Symbolic Logic, Tome 63 (1998) no. 1, pp.  51-58. http://gdmltest.u-ga.fr/item/1183745456/