Superstrong and other large cardinals are never Laver indestructible

摘要

Superstrong cardinals are never Laver indestructible. Similarly, almost huge cardinals, huge cardinals, superhuge cardinals, rank-into-rank cardinals, extendible cardinals, 1-extendible cardinals, 0-extendible cardinals, weakly superstrong cardinals, uplifting cardinals, pseudo-uplifting cardinals, superstrongly unfoldable cardinals, I pound (n) -reflecting cardinals, I pound (n) -correct cardinals and I pound (n) -extendible cardinals (all for n a parts per thousand yen 3) are never Laver indestructible. In fact, all these large cardinal properties are superdestructible: if kappa exhibits any of them, with corresponding target theta, then in any forcing extension arising from nontrivial strategically