User blog comment:Deedlit11/Extending the fast-growing hierarchy to nonrecursive ordinals/@comment-25418284-20130423064402/@comment-1605058-20130423102243

If by \(\Omega\) you mean \(\omega_1\), which is fixed point of every countable (mapping countable ordinals to countable ordinals) normal (increasing and continuous) function, then \(\omega_\Omega^\text{CK}=\Omega\).