Journal title
Archive for Mathematical Logic
DOI
10.1007/s00153-015-0458-3
Issue
1-2
Volume
55
Last updated
2022-02-17T04:18:48.983+00:00
Page
19-35
Abstract
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, Σn-reflecting cardinals, Σn-correct cardinals and Σn-extendible cardinals (all for n ≥ 3) are never Laver indestructible. In fact, all these large cardinal properties are superdestructible: if κ exhibits any of them, with corresponding target θ, then in any forcing extension arising from nontrivial strategically <κ-closed forcing (Formula presented.), the cardinal κ will exhibit none of the large cardinal properties with target θ or larger.
Symplectic ID
916658
Submitted to ORA
On
Publication type
Journal Article
Publication date
23 December 2015