User blog comment:Fejfo/Uncountable indexed veblen function/@comment-5529393-20180517062334

A few comments:

Your definition requires fundamental sequences, so those should be defined as well.

The rules can be strange if beta is an uncountable ordinal - for example, phi_omega (Omega) [n] = phi_n (Omega) = Omega, which is not a proper fundamental sequence. Perhaps you meant to restrict beta to countable ordinals.

If alpha has cofinality omega, then we will apply rule floor for beta < omega, and then rule 3 for beta >= omega. This leads to a rather odd demarcation at omega - for example, we get phi_omega (n) = phi_n (n) for n < omega, which is not what the normal Veblen function gives.