User blog comment:Deedlit11/Extending the fast-growing hierarchy to nonrecursive ordinals/@comment-25418284-20130423064402/@comment-25418284-20130424185304

Can we define \(\omega_\alpha^\text{CK}\) as an ordinal collapsing function? something like:


 * \(\omega_\alpha^\text{CK}\) is the smallest ordinal not constructible from finite applications of \(0\), \(1\), \(\omega\), \(\Omega\), \(\lim_{n \rightarrow \omega} \phi(n)\) for any partial recursive function \(\phi\), and previous values of \(\omega_\alpha^\text{CK}\)