User blog comment:Deedlit11/Extending the fast-growing hierarchy to nonrecursive ordinals/@comment-25418284-20130325203802/@comment-1605058-20130331120416

To be honest, I don't know how to translate this idea into trees. I think we can apply oracle to all of them (then this oracle must be strictly stronger, i.e. have strictly greater ordinal).

Only idea I had with second thing is exactly by induction. If there was easy way, it'd be straightforward to prove that all ordinals below Phi(1,0) are Xi-recursive