User blog comment:Deedlit11/Ordinal Notations III: Collapsing Higher Cardinalities/@comment-7484840-20130706154845/@comment-7484840-20130706183636

I was thinking that in the psi function, $$\psi_0(\Omega_{\Omega_3}) = \psi_0(\alpha\mapsto\psi_{\Omega_3}(\alpha))$$, and then $$\psi_{\Omega_3}(0) = \psi_{\alpha\mapsto\psi_2(\alpha)}(0)$$ or something.