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arXiv · 2505.05243

Power $\Sigma_1$ in Card with two Woodin cardinals

Farmer Schlutzenberg
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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 $x\mapsto P(x)$ being $\Sigma_1$-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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Farmer Schlutzenberg. 2025-05-08. Power $\Sigma_1$ in Card with two Woodin cardinals. https://arxiv.org/abs/2505.05243

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