User blog comment:Alemagno12/I made a Pi w-reflection OCF, how horribly wrong am I?/@comment-35470197-20180812220655

In your definition, \(\varepsilon\), \(\pi\), and \(\kappa\) are restricted to regular cardinals, right?

Also, in order to ensure the well-definedness of your functions \(M\) and \(\Psi\), you need to restrict the imput \(\gamma\) to be a sufficiently small ordinal. At least, \(M_{\kappa}^{P_0,A}(\alpha)\) for \(\alpha > |A|) is not well-defined.

For \(M_{\kappa}^{P_m+1,A}(\alpha)\), are you assuming \(\pi \in A\) as in \(M_{\kappa}^{P_0,A}(\alpha)\)? Also, are you assuming some condition on \(A \in C_n(\alpha,\beta)\)?