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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2307.13682 |
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| _version_ | 1866912454818136064 |
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| author | Aksornthong, Navin Gappo, Takehiko Holland, James Sargsyan, Grigor |
| author_facet | Aksornthong, Navin Gappo, Takehiko Holland, James Sargsyan, Grigor |
| contents | We show that in the $\mathbb{P}_{\max}$ extension of a certain Chang-type model of determinacy, if $κ\in\{ω_1, ω_2, ω_3\}$, then the restriction of the club filter on $κ\cap\mathrm{Cof}(ω)$ to HOD is an ultrafilter in HOD. This answers Question 4.11 of [BNH23] raised by Ben-Neria and Hayut. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_13682 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On $ω$-strongly measurable cardinals in $\mathbb{P}_{\max}$ extensions Aksornthong, Navin Gappo, Takehiko Holland, James Sargsyan, Grigor Logic We show that in the $\mathbb{P}_{\max}$ extension of a certain Chang-type model of determinacy, if $κ\in\{ω_1, ω_2, ω_3\}$, then the restriction of the club filter on $κ\cap\mathrm{Cof}(ω)$ to HOD is an ultrafilter in HOD. This answers Question 4.11 of [BNH23] raised by Ben-Neria and Hayut. |
| title | On $ω$-strongly measurable cardinals in $\mathbb{P}_{\max}$ extensions |
| topic | Logic |
| url | https://arxiv.org/abs/2307.13682 |