On ω-strongly measurable cardinals in ℙ_max extensions

2023/07/25 by Aksornthong, Navin, Gappo, Takehiko, Holland, James +1
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2307.13682

Abstract

We show that in the ℙ_max extension of a certain Chang-type model of determinacy, if κ∈\ω₁, ω₂, ω₃\, then the restriction of the club filter on κ\capCof(ω) to HOD is an ultrafilter in HOD. This answers Question 4.11 of [BNH23] raised by Ben-Neria and Hayut.

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