User blog comment:B1mb0w/Fundamental Sequences/@comment-5529393-20151113121456/@comment-10262436-20151115014548

There is some inconsistency here. Couple of Points:

(1) LittlePeng9 proved g=e_d and g^^w=e_d+1  this is phi(1,d)^^w = phi(1,d+1) and not phi(1,d)^^w = phi(1,phi(1,d)+1). I agree with this proof and it is consistent with my Rule 3.

(2) Don't think e_zeta_0 is well defined. I will add a detailed explanation of this in my blog. But in general, I don't think we assume any sequence of ordinals can be well-defined. We need to check how the sequence was generated before we can assume it is well defined.