User blog comment:Syst3ms/A formal definition for UNOCF/@comment-35470197-20180728080043/@comment-35470197-20180729072428

> In the case α=2I, then we apply the diagonalizer rule, not the inaccessible one.

Why? Do you have an explicit expression \(\ddots \kappa = 2^I\) using \(0, \Omega, +, \psi, C\) and so on?

Your rule says that you apply the diagonaliser rule only when \(\alpha = \ddots \kappa\) for some nested expression \(\ddots\). But there are only countably many such \(\alpha\)'s, if I correctly understand what you mean by "nesting". Then there is an \(\alpha\) with \(\alpha = \Omega_{\alpha} > \kappa \geq I\), for which \(\psi_{\kappa}(\alpha)\) is not defined in your rules.