On ω-strongly measurable cardinals in Pmax extensions

被引：0

作者：

Aksornthong, Navin ^{[1
]}

Gappo, Takehiko ^{[2
]}

Holland, James

Sargsyan, Grigor ^{[3
]}

机构：

[1] Hill Ctr Busch Campus, 110 Frelinghuysen Rd, Piscataway, NJ 08854 USA

[2] TU Wien, Inst Diskrete Math & Geometrie, Wiedner Hauptstr 8-10-104, A-1040 Vienna, Austria

[3] IMPAN, Antoniego Abrahama 18, PL-81825 Sopot, Poland

来源：

JOURNAL OF MATHEMATICAL LOGIC | 2024年

基金：

奥地利科学基金会;

关键词：

Inner model theory; determinacy; HOD conjecture; omega-strongly measurable cardinals; P-max forcing;

D O I：

10.1142/S0219061324500181

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that in the P-max extension of a certain Chang-type model of determinacy, if kappa is an element of {omega(1), omega(2), omega(3)}, then the restriction of the club filter on kappa boolean AND Cof(omega) to HOD is an ultrafilter in HOD. This answers Question 4.11 of [O. Ben-Neria and Y. Hayut, On omega-strongly measurable cardinals, Forum Math. Sigma 11 (2023) e19].

引用

页数：26

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