User:Googleaarex/Beyond Church-Kleene ordinal

For \(\omega^{ck}_1\), this is Church-Kleene_ordinal, then \(\omega^{ck}_2\), \(\omega^{ck}_\omega\), \(\omega^{ck}_{\varepsilon_0}\), \(\omega^{ck}_{\Gamma_0}\), \(\omega^{ck}_{\theta(\Omega^\Omega)}\), \(\omega^{ck}_{\theta(^\omega\Omega)}\), \(\omega^{ck}_{\omega^{ck}_{1}}\), \(\omega^{ck}_{\omega^{ck}_{\omega^{ck}_{1}}}\), etc.

For \(\alpha \rightarrow \omega^{ck}_\alpha\), this is Goucher ordinal, I called \(\varphi^{ck}(1,0)\).

For \(\varphi^{ck}(1,m)\), this is \(\omega^{ck}_{...{\varphi^{ck}(1,m-1)}}\)