User blog comment:Deedlit11/Ordinal Notations IV: Up to a weakly inaccessible cardinal/@comment-11227630-20170301040811

I get $$\psi_\Omega(\alpha)=\Gamma_\alpha$$ for $$\alpha<\Omega$$.

Then $$\psi_\Omega(\Omega)=\Omega$$, and the "$$\{\beta<\pi|C(\alpha,\beta)\cap\pi\subseteq\beta\wedge\pi\in C(\alpha,\beta)\}$$" is empty set.

If it works in the $$\vartheta$$-way, the $$\psi_\Omega(\varphi(1,1,0))$$ should be $$\psi_\Omega(\Gamma_{\varphi(1,1,0)+1})$$, and $$\psi_\Omega(\Omega)$$ should be $$\varphi(1,1,0)$$, I guess.