User blog comment:Tetramur/Pentational arrays and beyond - comparisons/@comment-37993808-20191211162933/@comment-35470197-20191212122539

@Triakula

Since the OP mentioned to the ordinal corresponding to BB, it just means "the ordinal α such that BB is comparable to f_α", which is ill-defined. If we are talking about computable functions of mild level, then such an "order" makes sense because of the existence of canonical fundamental sequences and the linearity of FGH in that realm, but the same does not hold in the realm of ω_1^{CK}.

It is not a weird property of ω_1^{CK} itself, but is due to the lack of canonical fundamental sequences which behave good.

Anyway, BEAF is not an uncomputable function. It is originally just ill-defined above tetration, although there are several candidates of alternative definitions up to pentation level, which are computale.