User blog comment:P進大好きbot/Rathjen-type Ordinal Notation/@comment-39259101-20190819131438/@comment-35470197-20190820154720

I guess that you got the wrong estimation of \(\psi_0(\Omega_1^{\omega})\) because you forgot that it is an non-standard expression or you applied the equality \(\psi_0(\alpha+1) = \psi_0(\alpha) + \omega\) to non-standard expressions.