## FANDOM

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An ordinal is called to be admissible if $$L_\alpha$$ is an admissible set, where $$L$$ is Gödel's constructible universe.[1] For successor ordinal $$\alpha$$, $$1+\alpha$$-th admissible ordinal is denoted by $$\omega_\alpha^\text{CK}$$. For example, $$\omega_\omega^\text{CK}$$ is not admissible but it is a limit of admissibles.

## Sources

1. Gostanian, Richard. The next admissible ordinal.