Chang models over derived models with supercompact measures

Takehiko Gappo; Sandra Müller; Grigor Sargsyan

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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 $\delta$ that is both a limit of Woodin cardinals and a limit of ${<}\delta$-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 $\mathsf{AD}_{\mathbb{R}} + \Theta$ is regular + $\omega_1$ is ${<}\delta_{\infty}$-supercompact for some regular cardinal $\delta_{\infty}>\Theta$. This complements Woodin's generalized Chang model, which satisfies $\mathsf{AD}_{\mathbb{R}}+\omega_1$ is supercompact, assuming a proper class of Woodin cardinals that are limits of Woodin cardinals.

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BibTeX RIS

Takehiko Gappo, Sandra Müller, Grigor Sargsyan. 2023-07-17. Chang models over derived models with supercompact measures. https://arxiv.org/abs/2307.08607

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