On the powersets of singular cardinals in hod

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

Research output: Contribution to journalArticlepeer-review


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.

Original languageAmerican English
Pages (from-to)1777-1789
Number of pages13
JournalProceedings of the American Mathematical Society
Issue number4
StatePublished - 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).

Publisher Copyright:
© 2020 American Mathematical Society


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