Church–Kleene ordinal

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In mathematics, the Church–Kleene ordinal, \omega^{\mathrm{CK}}_1, named after Alonzo Church and S. C. Kleene, is a large countable ordinal. It is the set of all recursive ordinals and the smallest non-recursive ordinal. It is also the first ordinal which is not hyperarithmetical, and the first admissible ordinal after ω.