The failure of GCH at a degree of supercompactness

Details The failure of GCH at a degree of supercompactness The failure of GCH at a degree of supercompactness

2011-10-24

arxiv.org/abs/1110.5365v2

Mathematics

Logic

Scientific paper

We determine the large cardinal consistency strength of the existence of a \lambda-supercompact cardinal \kappa such that GCH fails at lambda. Indeed, we show that the existence of a \lambda-supercompact cardinal \kappa\ such that 2^\lambda\ \geq \theta\ is equiconsistent with the existence of a \lambda-supercompact cardinal that is also \theta-tall. We also prove some basic facts about the large cardinal notion of tallness with closure.

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