User blog comment:Wythagoras/Catching function in normal ordinals/@comment-11227630-20140203095754/@comment-5150073-20140626142809

Peng, really, why? There's a computable and recursive way to define all FS's up to, say, $$\psi(\psi_I(0))$$. If Hyp cos all correct, SGH meets FGH exactly $$\omega$$ times up to this point, and so $$C(\omega^2)$$ is undefined and thereby $$C(\alpha)$$ is partial for any recursive definition.