 The “I” in the foregoing notation is supposed to be indicative of “inaccessible cardinal”. Indeed, the easiest way to build an extended ordinal representation system sufficient unto this task (modeled on  Definition 5.11)  is to add an inaccessible I, close the Skolem hulls under \(\xi\mapsto \Omega_\xi\) for \(\xi&lt;I\) and introduce collapsing functions \(\psi_{\pi}\) for all \(\pi\) of either form I or \(\Omega_{\xi+1}\).