Diamond (on the regulars) can fail at any strongly unfoldable cardinal

Annals of Pure and Applied Logic 144 (1):83-95 (2006)
Authors
Joel David Hamkins
Oxford University
Abstract
If κ is any strongly unfoldable cardinal, then this is preserved in a forcing extension in which κ fails. This result continues the progression of the corresponding results for weakly compact cardinals, due to Woodin, and for indescribable cardinals, due to Hauser
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DOI 10.1016/j.apal.2006.05.001
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References found in this work BETA

The Lottery Preparation.Joel David Hamkins - 2000 - Annals of Pure and Applied Logic 101 (2-3):103-146.
Indescribable Cardinals and Elementary Embeddings.Kai Hauser - 1991 - Journal of Symbolic Logic 56 (2):439-457.
Chains of End Elementary Extensions of Models of Set Theory.Andrés Villaveces - 1998 - Journal of Symbolic Logic 63 (3):1116-1136.
A Note on Extensions of Infinitary Logic.Saharon Shelah & Jouko Väänänen - 2004 - Archive for Mathematical Logic 44 (1):63-69.
Unfoldable Cardinals and the GCH.Joel David Hamkins - 2001 - Journal of Symbolic Logic 66 (3):1186-1198.

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Citations of this work BETA

Strongly Unfoldable Cardinals Made Indestructible.Thomas A. Johnstone - 2008 - Journal of Symbolic Logic 73 (4):1215-1248.
Diagonal Reflections on Squares.Gunter Fuchs - forthcoming - Archive for Mathematical Logic:1-26.
Partial Near Supercompactness.Jason Aaron Schanker - 2013 - Annals of Pure and Applied Logic 164 (2):67-85.

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