User blog comment:Googleaarex/Unlimitable Ordinals/@comment-25418284-20130823215256/@comment-10429372-20130825064440

I'm not sure, but I think he means that limit of alpha = omega^alpha = phi_1(0)

Limit of two entry phi-function = limit of limit of alpha = omega^alpha = gamma_0

I also think that

UL(4)[n] = theta(Omega^omega)[n],

UL(5)[n] = theta(Omega^Omega)[n] and

UL(6)[n] = BHO[n]

It is interesting that Y(n) ~ f_UL(n-1)(n)

( Y(n) is my function which diagonalize through all possible array notations using n rules, e.g. Y(3) uses bracket notation beacause bracket notation is the strongest (known) notation using 3 rules)