User blog comment:Wythagoras/FGH of Array Notations/@comment-7484840-20130708081724/@comment-5529393-20130709060124

I is not Omega_Omega_Omega..., it is inconceivably larger. Basically it is similar to Omega:  Omega is unreachably larger than any recursive construction on countable ordinals,  but we "collapse" Omega and larger ordinals down to countable ordinals using one of our collapsing functions. Similarly, we use I to generate a hierarchy based on alpha -> Omega_alpha.

psi_I(0) is Omega_Omega_Omega..., and psi_I(alpha) is the 1+alphath fixed point of a -> Omega_a. psi_I(I) diagonalizes over psi_I(alpha), i.e. it is the smallest ordinal beta such that beta = psi_I(beta), and the hierarchy continues in similar fashion to the Omega hierarchy.

When you mentioned that your notation went up to the SVO based on the Omega_a function, I believe you were talking about psi_I(I^w).