User blog comment:Testitemqlstudop/FPT, large ordinals, ordinal FGH and a new Fundamental Sequence system/@comment-35470197-20191031122541/@comment-35470197-20191031134246

It is actually the diagonalisation of the sequence, but is not the ω-th entry.

I guess that you understood ordinals below φ_ω(0). Have you studied Veblen function? If not yet, it is good to study it, because Veblen function give a clearer vision of the sequence epsilon_0, zeta_0, eta_0, ... .