تقرير
Chang models over derived models with supercompact measures
العنوان: | Chang models over derived models with supercompact measures |
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المؤلفون: | Gappo, Takehiko, Müller, Sandra, Sargsyan, Grigor |
سنة النشر: | 2023 |
المجموعة: | Mathematics |
مصطلحات موضوعية: | Mathematics - Logic |
الوصف: | 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. Comment: 22 pages |
نوع الوثيقة: | Working Paper |
URL الوصول: | http://arxiv.org/abs/2307.08607 |
رقم الأكسشن: | edsarx.2307.08607 |
قاعدة البيانات: | arXiv |
الوصف غير متاح. |