The failure of GCH at a degree of supercompactness

نویسنده

Brent Cody

چکیده

We determine the large cardinal consistency strength of the existence of a λ-supercompact cardinal κ such that GCH fails at λ. Indeed, we show that the existence of a λ-supercompact cardinal κ such that 2 ≥ 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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