Superstrong and other large cardinals are never Laver indestructible

作者：Bagaria Joan^*; Hamkins Joel David; Tsaprounis Konstantinos; Usuba Toshimichi

来源：Archive for Mathematical Logic, 2016, 55(1-2): 19-35.

DOI：10.1007/s00153-015-0458-3

• Large cardinals
• Forcing
• Indestructible cardinals

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 <kappa-closed forcing , the cardinal kappa will exhibit none of the large cardinal properties with target theta or larger.

• 出版日期2016-2