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

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	American 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

Bibliographical note

Funding Information:
Received by the editors September 2, 2018, and, in revised form, August 30, 2019. 2010 Mathematics Subject Classification. Primary 03E10, 03E35, 03E45, 03E55. This work is based upon research supported by the National Science Foundation under Grants No. DMS-1363364, DMS-1764029 (Neeman), DMS-1700425 (Unger), and DMS-1800613 (Ben-Neria), and the Israel Science Foundation Grant No. 58/14 (Gitik).

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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.",

author = "Omer Ben-Neria and Moti Gitik and Itay Neeman and Spencer Unger",

note = "Funding Information: Received by the editors September 2, 2018, and, in revised form, August 30, 2019. 2010 Mathematics Subject Classification. Primary 03E10, 03E35, 03E45, 03E55. This work is based upon research supported by the National Science Foundation under Grants No. DMS-1363364, DMS-1764029 (Neeman), DMS-1700425 (Unger), and DMS-1800613 (Ben-Neria), and the Israel Science Foundation Grant No. 58/14 (Gitik). Publisher Copyright: {\textcopyright} 2020 American Mathematical Society",

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AU - Unger, Spencer

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On the powersets of singular cardinals in hod

Abstract

Bibliographical note

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