User blog comment:Deedlit11/Extending the fast-growing hierarchy to nonrecursive ordinals/@comment-25418284-20130325203802/@comment-5529393-20130331113603

I'm afraid I still don't follow. If we construct all trees with rank \(\omega_{\alpha}^{CK}\), how do we apply the Ω operator to all of them? We need a single tree with a rank of \(\omega_{\alpha+1}^{CK}\). Also, given that \(\alpha\) is Xi-recursive, how do we conclude that \(\omega_{\alpha}^{CK}\) is Xi-recursive? Thanks for your help explaining.