The Ultrapower Axiom and the equivalence between strong compactness and supercompactness
Logic
2018-10-12 v1
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.
Cite
@article{arxiv.1810.05058,
title = {The Ultrapower Axiom and the equivalence between strong compactness and supercompactness},
author = {Gabriel Goldberg},
journal= {arXiv preprint arXiv:1810.05058},
year = {2018}
}