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Chang models over derived models with supercompact measures
- Publication Year :
- 2023
-
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 $\mathsf{AD}^+ + \mathsf{AD}_{\mathbb{R}} + \Theta$ is regular + $\omega_1$ is ${<}\delta_{\infty}$-supercompact for some regular cardinal $\delta_{\infty}>\Theta$. This complements Woodin's generalized Chang model, which satisfies $\mathsf{AD}^+ + \mathsf{AD}_{\mathbb{R}}+\omega_1$ is supercompact, assuming a proper class of Woodin cardinals that are limits of Woodin cardinals.<br />Comment: 22 pages
- Subjects :
- Mathematics - Logic
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2307.08607
- Document Type :
- Working Paper