The *Church-Kleene* ordinal $\omega_1^{ck}$ is the supremum of the computable ordinals, where an ordinal $\alpha$ is *computable* if there is a computable relation $\lhd$ on $\mathbb{N}$ of order type $\alpha$, that is, such that $\langle\alpha,\lt\rangle\cong\langle\mathbb{N},\lhd\rangle$. This ordinal is closed under all of the elementary ordinal arithmetic operations, such as successor, addition, multiplication and exponentiation. The Church-Kleene ordinal is the least [admissible](Admissible%20ordinal.md "Admissible") ordinal. ## Relativized Church-Kleene ordinal The Church-Kleene idea easily relativizes to oracles, where for any real $x$, we define $\omega_1^x$ to be the supremum of the $x$-computable ordinals. This is also the least [admissible](Admissible%20ordinal.md "Admissible") ordinal relative to $x$, and every countable successor admissible ordinal is $\omega_1^x$ for some $x$. This article is a stub. Please help us to improve Cantor's Attic by adding information.