Name
Abstract | ||
|---|---|---|
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, Σ n -reflecting cardinals, Σ n -correct cardinals and Σ n -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 \({\mathbb{Q} \in V_\theta}\), the cardinal κ will exhibit none of the large cardinal properties with target θ or larger. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1007/s00153-015-0458-3 | Archive for Mathematical Logic |
Keywords | Field | DocType |
Large cardinals,Forcing,Indestructible cardinals | Discrete mathematics,Combinatorics,Large cardinal,Cardinal number,Forcing (mathematics),Mathematics | Journal |
Volume | Issue | ISSN |
55 | 1 | 1432-0665 |
Citations | PageRank | References |
10 | 1.00 | 14 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Joan Bagaria | 1 | 63 | 13.15 |
| Joel Hamkins | 2 | 373 | 77.55 |
| Konstantinos Tsaprounis | 3 | 17 | 3.09 |
| Toshimichi Usuba | 4 | 14 | 4.99 |