2018/10/09 by Goldberg, Gabriel
#FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1810.05058
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.