User blog comment:Kyodaisuu/Mashimo function/@comment-1605058-20140706065714/@comment-24061664-20140707053207

I found description in Wikipedia "By a theorem of Sacks, the countable admissible ordinals are exactly those constructed in a manner similar to the Church-Kleene ordinal but for Turing machines with oracles. One sometimes writes w_a^CK for the a-th ordinal that is either admissible or a limit of admissible." It is therefore straightforward to define w_a+1^CK from TM with w_a^CK oracle.