Church-Kleene ordinal

The \(\omega^text{CK}_1\) (called "Church-Kleene ordinal") is the first non-recursive ordinal. In any well-defined hierarchy \(R_{\omega^text{CK}_1}(n)\), eventually overgrows any computable function.

It is the ordinal that measures complexity of the, and thereby \(R_{\omega^text{CK}_1}(n)\) should be on par with \(\Sigma(n)\), the busy beaver function.