Power 1 in Card with two Woodin cardinals
Abstract
V\"a\"an\"anen and Welch asked in the paper "When cardinals determine the power set: inner models and H\"artig quantifier logic" which large cardinals are consistent with the power set operation x P(x) being 1-definable in the predicate Card of all cardinals. We show that, relative to large cardinals, this property is consistent together with the existence of two Woodin cardinals.
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