The Ultrapower Axiom and the equivalence between strong compactness and supercompactness

Gabriel Goldberg

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arXiv · 1810.05058

The Ultrapower Axiom and the equivalence between strong compactness and supercompactness

Gabriel Goldberg

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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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BibTeX RIS

Gabriel Goldberg. 2018-10-09. The Ultrapower Axiom and the equivalence between strong compactness and supercompactness. https://arxiv.org/abs/1810.05058

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