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arXiv · 2307.08607

Chang models over derived models with supercompact measures

Takehiko Gappo·Sandra Müller·Grigor Sargsyan
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Abstract

Based on earlier work of the third author, we construct a Chang-type model with supercompact measures extending a derived model of a given hod mouse with a regular cardinal $δ$ that is both a limit of Woodin cardinals and a limit of ${<}δ$-strong cardinals. The existence of such a hod mouse is consistent relative to a Woodin cardinal that is a limit of Woodin cardinals. We argue that our Chang-type model satisfies $\mathsf{AD}_{\mathbb{R}} + Θ$ is regular + $ω_1$ is ${<}δ_{\infty}$-supercompact for some regular cardinal $δ_{\infty}>Θ$. This complements Woodin's generalized Chang model, which satisfies $\mathsf{AD}_{\mathbb{R}}+ω_1$ is supercompact, assuming a proper class of Woodin cardinals that are limits of Woodin cardinals.

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Takehiko Gappo, Sandra Müller, Grigor Sargsyan. 2025-02-13. Chang models over derived models with supercompact measures. https://arxiv.org/abs/2307.08607

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