Superstrong and other large cardinals are never Laver indestructible

Joan Bagaria, Joel David Hamkins, Konstantinos Tsaprounis, Toshimichi Usuba

Research output: Contribution to journalArticle

2 Citations (Scopus)

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

Original languageEnglish
Pages (from-to)19-35
Number of pages17
JournalArchive for Mathematical Logic
Volume55
Issue number1-2
DOIs
Publication statusPublished - 2016 Feb 1
Externally publishedYes

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Large Cardinals
Forcing
Target

Keywords

  • Forcing
  • Indestructible cardinals
  • Large cardinals

ASJC Scopus subject areas

  • Logic
  • Philosophy

Cite this

Superstrong and other large cardinals are never Laver indestructible. / Bagaria, Joan; Hamkins, Joel David; Tsaprounis, Konstantinos; Usuba, Toshimichi.

In: Archive for Mathematical Logic, Vol. 55, No. 1-2, 01.02.2016, p. 19-35.

Research output: Contribution to journalArticle

Bagaria, Joan ; Hamkins, Joel David ; Tsaprounis, Konstantinos ; Usuba, Toshimichi. / Superstrong and other large cardinals are never Laver indestructible. In: Archive for Mathematical Logic. 2016 ; Vol. 55, No. 1-2. pp. 19-35.
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