The failure of GCH at a degree of supercompactness

Mathematical Logic Quarterly 58 (1):83-94 (2012)
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Abstract

We determine the large cardinal consistency strength of the existence of a λ-supercompact cardinal κ such that equation image fails at λ. Indeed, we show that the existence of a λ-supercompact cardinal κ such that 2λ ≥ θ is equiconsistent with the existence of a λ-supercompact cardinal that is also θ-tall. We also prove some basic facts about the large cardinal notion of tallness with closure

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Citations of this work

On supercompactness and the continuum function.Brent Cody & Menachem Magidor - 2014 - Annals of Pure and Applied Logic 165 (2):620-630.

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References found in this work

[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
The lottery preparation.Joel David Hamkins - 2000 - Annals of Pure and Applied Logic 101 (2-3):103-146.
The negation of the singular cardinal hypothesis from o(K)=K++.Moti Gitik - 1989 - Annals of Pure and Applied Logic 43 (3):209-234.
Tall cardinals.Joel D. Hamkins - 2009 - Mathematical Logic Quarterly 55 (1):68-86.

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