User blog comment:DrCeasium/Hyperfactorial array notation: Analysis part 3/@comment-5529393-20130530121945/@comment-7484840-20130530142905

As far as I can see, the higher level ordinal collapsing functions work just like the lower ones, but instead of collapsing level-1 Omegas into huge countable ordinals, they do exactly the same process to level-(k+1) Omegas to generate huge level-k-omega-structures: for example:

psi_0(Omega_1) = psi(Omega) = zeta_0. ( = alpha |--> psi(alpha))

psi_3(Omega_4) = zeta_{Omega_3+1}  ( = alpha |--> psi_3(alpha))

And the rule for Omegas is that psi_{k}(@Omega_{k+1}@) = alpha |-->  psi_{k}(@alpha@), assuming the Omega is the one that should be worked on: not to the power of anything or multiplied by anything etc.

is this correct?