Critical cardinals

Yair Hayut, Asaf Karagila*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


We introduce the notion of a critical cardinal as the critical point of sufficiently strong elementary embedding between transitive sets. Assuming the Axiom of Choice this is equivalent to measurability, but it is wellknown that Choice is necessary for the equivalence. Oddly enough, this central notion was never investigated on its own before. We prove a technical criterion for lifting elementary embeddings to symmetric extensions, and we use this to show that it is consistent relative to a supercompact cardinal that there is a critical cardinal whose successor is singular.

Original languageAmerican English
Pages (from-to)449-472
Number of pages24
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - 1 Mar 2020
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2020, The Hebrew University of Jerusalem.


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