Inner Models from Extended Logics: Part 2
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2020
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| _version_ | 1866909100694044672 |
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| author | Kennedy, Juliette Magidor, Menachem Väänänen, Jouko |
| author_facet | Kennedy, Juliette Magidor, Menachem Väänänen, Jouko |
| contents | We introduce a new inner model $C(aa)$ arising from stationary logic. We show that assuming a proper class of Woodin cardinals, or alternatively $MM^{++}$, the regular uncountable cardinals of $V$ are measurable in the inner model $C(aa)$, the theory of $C(aa)$ is (set) forcing absolute, and $C(aa)$ satisfies CH. We introduce an auxiliary concept that we call club determinacy, which simplifies the construction of $C(aa)$ greatly but may have also independent interest. Based on club determinacy, we introduce the concept of aa-mouse which we use to prove CH and other properties of the inner model $C(aa)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2007_10766 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Inner Models from Extended Logics: Part 2 Kennedy, Juliette Magidor, Menachem Väänänen, Jouko Logic 03E45 We introduce a new inner model $C(aa)$ arising from stationary logic. We show that assuming a proper class of Woodin cardinals, or alternatively $MM^{++}$, the regular uncountable cardinals of $V$ are measurable in the inner model $C(aa)$, the theory of $C(aa)$ is (set) forcing absolute, and $C(aa)$ satisfies CH. We introduce an auxiliary concept that we call club determinacy, which simplifies the construction of $C(aa)$ greatly but may have also independent interest. Based on club determinacy, we introduce the concept of aa-mouse which we use to prove CH and other properties of the inner model $C(aa)$. |
| title | Inner Models from Extended Logics: Part 2 |
| topic | Logic 03E45 |
| url | https://arxiv.org/abs/2007.10766 |