On the powersets of singular cardinals in hod

Omer Ben-Neria; Moti Gitik; Itay Neeman; Spencer Unger

doi:10.1090/proc/14913

On the powersets of singular cardinals in hod

Omer Ben-Neria
, Moti Gitik
, Itay Neeman
, Spencer Unger

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We prove that the assertion “There is a singular cardinal κ such that for all x ⊆ κ, HOD_x does not contain the entire powerset of κ” is equiconsistent with the assertion that there is a cardinal κ such that {o(ν) | ν < κ} is unbounded in κ.

Original language	English
Pages (from-to)	1777-1789
Number of pages	13
Journal	Proceedings of the American Mathematical Society
Volume	148
Issue number	4
DOIs	https://doi.org/10.1090/proc/14913
State	Published - 2020

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© 2020 American Mathematical Society

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abstract = "We prove that the assertion “There is a singular cardinal κ such that for all x ⊆ κ, HODx does not contain the entire powerset of κ” is equiconsistent with the assertion that there is a cardinal κ such that \{o(ν) | ν < κ\} is unbounded in κ.",

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AB - We prove that the assertion “There is a singular cardinal κ such that for all x ⊆ κ, HODx does not contain the entire powerset of κ” is equiconsistent with the assertion that there is a cardinal κ such that {o(ν) | ν < κ} is unbounded in κ.

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On the powersets of singular cardinals in hod

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