User blog comment:Deedlit11/Ordinal Notations V: Up to a weakly Mahlo cardinal/@comment-35470197-20180808064240

Could you tell me the proof of your theorem \(\psi_{\Omega_1}(\varepsilon_{M+1}) = \textrm{PTO}(KPM)\)? Also, do you have a comparison result between your OCF and Rathjen's OCF?

I wonder why your OCF is so strong that it goes beyond \(\textrm{PTO}(KPM)\), although
 * you defined an OCF on the class of all ordinals, while Rathjen restricted the domain.
 * you did not use the function \(\kappa \mapsto \kappa^{-}\) in Rathjen's OCF. (I know that we do not need \(Phi\), but do not know about \(\kappa^{-}\).\)