A worldly cardinal is a cardinal $\kappa$ such that $V_\kappa$ is a model of $\mathsf{ZFC}$. Please forgive me if this is very silly, but if $\mathsf{ZFC}$ is consistent (so there exists a model of $\mathsf{ZFC}$), must there exists a model of the form $V_\kappa$? Please note that I'm not asking about the existence of an inaccessible cardinal, which I know is not granted according to this question. Any help appreciated.
2026-03-29 02:11:09.1774750269
Does worldly cardinal exist if $\mathsf{ZFC}$ is consistent?
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