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The failure of GCH at a degree of supercompactness
Author(s) -
Cody Brent
Publication year - 2012
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201020078
Subject(s) - mathematics , closure (psychology) , consistency (knowledge bases) , degree (music) , regular cardinal , pure mathematics , combinatorics , discrete mathematics , physics , economics , acoustics , market economy
We determine the large cardinal consistency strength of the existence of a λ‐supercompact cardinal κ such that \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathsf {GCH}$\end{document} fails at λ. Indeed, we show that the existence of a λ‐supercompact cardinal κ such that 2 λ ≥ 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.