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

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
Keywords tall cadinals  Large cardinals  forcing  generalized continuum hypothesis  03E35  MSC (2010) 03E55  supercompact cardinals  \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathsf {GCH}$\end{document}
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DOI 10.1002/malq.201020078
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References found in this work BETA

[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++.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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Citations of this work BETA

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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