Critical Cardinals

Yair Hayut, Asaf Karagila

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
17 Downloads (Pure)


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 well-known 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 languageEnglish
Pages (from-to)449–472
Number of pages24
JournalIsrael Journal of Mathematics
Issue number1
Early online date4 Apr 2020
Publication statusPublished - Apr 2020

Cite this