User blog comment:Boboris02/Boris's ultima function/@comment-24676271-20161104001226/@comment-1605058-20161104120349

For any ordinal $$\alpha<\omega_1^\text{CK}$$ we can extend FGH up to $$f_\alpha$$ such that all the functions are computable. Also, as Aarex mentions, there are ordinals larger than $$\psi(\psi_I(0))$$, and there are such ordinals which are well below $$\omega_1^\text{CK}$$, so I don't know what you mean with "it is the largest limit ordinal for computable functions".