nLab limit club Berkeley cardinal

Idea

A large cardinal stronger than Reinhardt cardinals that is inconsistent with ZF with countable choice. In order to remove the inconsistency, one has to remove the axiom of countable choice to get bare ZF + a limit club Berkeley cardinal.

Definition

In ZF, a cardinal $\delta$ is a limit club Berkeley cardinal if it is a club Berkeley cardinal and it is the limit cardinal of club Berkeley cardinals.

Related concepts

• large cardinal

• elementary embedding

• club Berkeley cardinal

References

• Joan Bagaria, Peter Koellner, W. Hugh Woodin: Large Cardinals Beyond Choice, The Bulletin of Symbolic Logic, Vol. 25, No. 3 (September 2019), pp. 283-318 (36 pages) [jstor:stable/26788522]

• Is there a largest large cardinal?, Mathematics Stackexchange, (web)