Record link: 
http://hdl.handle.net/20.500.12708/224770
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Title: 
On ω-strongly measurable cardinals in ℙmax extensions
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Citation: 
Aksornthong, N., Gappo, T., Holland, J., & Sargsyan, G. (2025). On ω-strongly measurable cardinals in ℙmax extensions. Journal of Mathematical Logic, 25(2), Article 2450018. https://doi.org/10.1142/S0219061324500181
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Publisher DOI: 
10.1142/S0219061324500181
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Publication Type: 
Article - Original Research Article
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Language: 
English
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Authors: 
Aksornthong, Navin 
Gappo, Takehiko 
Holland, James 
Sargsyan, Grigor 
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Organisational Unit: 
E104-08 - Forschungsbereich Mengenlehre 
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Journal: 
Journal of Mathematical Logic 
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ISSN: 
0219-0613
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Date (published): 
Aug-2025
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Number of Pages: 
26
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Publisher: 
WORLD SCIENTIFIC PUBL CO PTE LTD
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Peer reviewed: 
Yes
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Keywords: 
determinacy; HOD conjecture; Inner model theory; ω-strongly measurable cardinals; ℙmax forcing
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Abstract: 
We show that in the Pmax extension of a certain Chang-type model of determinacy, if κ ∈ {ω₁, ω₂, ω₃}, then the restriction of the club filter on κ ∩ Cof(ω) to HOD is an ultrafilter in HOD. This answers Question 4.11 of [O. Ben-Neria and Y. Hayut, On ω-strongly measurable cardinals, Forum Math. Sigma 11 (2023) e19].
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Project title: 
Klassifikation abgeleiteter Modelle der Determiniertheit: I6087-N (FWF - Österr. Wissenschaftsfonds) 
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Research Areas: 
Fundamental Mathematics Research: 100%
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Science Branch: 
1010 - Mathematik: 100%
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