Journal of Symbolic Logic

Strongly unfoldable cardinals made indestructible

Thomas A. Johnstone

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Abstract

I provide indestructibility results for large cardinals consistent with V=L, such as weakly compact, indescribable and strongly unfoldable cardinals. The Main Theorem shows that any strongly unfoldable cardinal κ can be made indestructible by < κ-closed, κ-proper forcing. This class of posets includes for instance all < κ-closed posets that are either κ⁺-c.c. or ≤ κ-strategically closed as well as finite iterations of such posets. Since strongly unfoldable cardinals strengthen both indescribable and weakly compact cardinals, the Main Theorem therefore makes these two large cardinal notions similarly indestructible. Finally, I apply the Main Theorem to obtain a class forcing extension preserving all strongly unfoldable cardinals in which every strongly unfoldable cardinal κ is indestructible by < κ-closed, κ-proper forcing.

Article information

Source
J. Symbolic Logic, Volume 73, Issue 4 (2008), 1215-1248.

Dates
First available in Project Euclid: 27 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1230396915

Digital Object Identifier
doi:10.2178/jsl/1230396915

Mathematical Reviews number (MathSciNet)
MR2467213

Zentralblatt MATH identifier
1168.03039

Subjects
Primary: 03E55: Large cardinals 03E40: Other aspects of forcing and Boolean-valued models

Keywords
strongly unfoldable cardinal forcing indestructibility

Citation

Johnstone, Thomas A. Strongly unfoldable cardinals made indestructible. J. Symbolic Logic 73 (2008), no. 4, 1215--1248. doi:10.2178/jsl/1230396915. https://projecteuclid.org/euclid.jsl/1230396915


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