Mice with Woodin cardinals from a Reinhardt

Farmer Schlutzenberg

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arXiv · 2402.04065

Mice with Woodin cardinals from a Reinhardt

Farmer Schlutzenberg

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Abstract

Suppose there is a Reinhardt cardinal. Then (1) $M_n(X)$ exists and is fully iterable (above $X$) for every transitive set $X$ and every $n<\omega$ (here $M_n(X)$ denotes the canonical minimal proper class inner model containing $X$ and having $n$ Woodin cardinals above the rank of $X$); and (2) Projective Determinacy holds in every set generic extension.

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Farmer Schlutzenberg. 2024-02-06. Mice with Woodin cardinals from a Reinhardt. https://arxiv.org/abs/2402.04065

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