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Bibliographic Details
Main Authors: Aksornthong, Navin, Gappo, Takehiko, Holland, James, Sargsyan, Grigor
Format: Preprint
Published: 2023
Subjects:
Online Access:https://arxiv.org/abs/2307.13682
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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