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The failure of GCH at a degree of supercompactness

โœ Scribed by Brent Cody

Publisher
John Wiley and Sons
Year
2012
Tongue
English
Weight
220 KB
Volume
58
Category
Article
ISSN
0044-3050

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โœฆ Synopsis

Abstract

We determine the large cardinal consistency strength of the existence of a ฮปโ€supercompact cardinal ฮบ such that \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathsf {GCH}$\end{document} fails at ฮป. Indeed, we show that the existence of a ฮปโ€supercompact cardinal ฮบ such that 2^ฮป^ โ‰ฅ ฮธ is equiconsistent with the existence of a ฮปโ€supercompact cardinal that is also ฮธโ€tall. We also prove some basic facts about the large cardinal notion of tallness with closure.

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