An ordinal $\gamma$ is admissible if the $L_\gamma$ level of the constructible universe satisfies the Kripke-Platek axioms of set theory.
The smallest admissible ordinal is $\omega_1^{ck}$, the least non-computable ordinal. More generally, for any real $x$, the least ordinal not computable from $x$ is denoted $\omega_1^x$, and is also admissible. Indeed, one has $L_{\omega_1^x}[x]\models\text{KP}$.
An ordinal $\alpha$ is computably inaccessible, also known as recursively inaccessible, if it is admissible and a limit of admissible ordinals.
    This article is a stub. Please help us to improve Cantor's Attic by adding information.