User blog comment:Syst3ms/A formal definition for UNOCF/@comment-35470197-20180728080043/@comment-35470197-20180728091613

Thank you. But how about the cofinality of \(\psi_{\kappa}(\alpha)\) for a limit ordinal \(\akpha\)? Since you defined the limit case directly by the Scott continuity, your table of cofinality does not tell us the cofinality of \(\psi_{\kappa}(\alpha)\).

Moreover, I could not understand what you explained in the diagonaliser rule. Since you have already defined the successor rule and the limit rule, there should not be additional rule unless you verify the compatibility.

Further, what does the diagonaliser rule mean? You defined \(\psi_{\kappa}(\ddot \kappa)\) as a function \(alpha \mapsto \psi_{\kappa}(\ddot \alpha)\), which is no longer an ordinal, right?