User blog:C7X/Extended Madore Psi

Is this a good definition of the extension of Madore's Psi Function?

\(C_{0,\zeta}(\alpha) = \{0,1,\Omega_{\zeta+1},\iota:\iota\le\Omega_\zeta\} \\ C_{n+1,\zeta}(\alpha)= \{\mu+\nu,\mu\nu,\mu^\nu,\psi_{\mu_2}(\vartheta) : \mu,\mu_2,\nu\in C_{n,\zeta}(\alpha)\land (\mu_2\le\zeta\implies\vartheta<\alpha)\} \\ C_{\zeta}(\alpha) = \bigcup_{n<\omega}C_{n,\zeta}(\alpha) \\ \psi_{\zeta}(\alpha) = \min\{\iota:\iota\notin C_{\zeta}(\alpha)\}\)