User blog comment:Username5243/Hedrondude just updated his large number pages/@comment-1605058-20160202140040/@comment-27173506-20160202172343

I too do not entirely trust non recursive growth rates, but w_1^CK is still more logical than w_1: which by definition has no fundamental sequence! (I'm talking about "natural" fundamental sequences, such that \(\alpha=\sup \lbrace \alpha \text{[n]} \rbrace\) for finite n, not stuff like \(\Omega [\alpha] = \alpha\))