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The Ultrapower Axiom and the equivalence between strong compactness and supercompactness

2018/10/09 by Goldberg, Gabriel
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1810.05058

Abstract

The relationship between the large cardinal notions of strong compactness and supercompactness cannot be determined under the standard ZFC axioms of set theory. Under a hypothesis called the Ultrapower Axiom, we prove that the notions are equivalent except for a class of counterexamples identified by Menas. This is evidence that strongly compact and supercompact cardinals are equiconsistent.

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