User blog comment:Flitri/An ordinal Collapsing up to the Least weakly Mahlo Cardinal/@comment-35470197-20190409053305/@comment-35470197-20190410035035

I could not understand whether it is sufficient or not. In order to set normal forms, you need to verify the uniqueness of a normal form of a given ordinal. For example, in Rathjen's original OCF, the author verified the images of \(\chi\) and \(\psi\) are disjoint.

I guess that it is not sufficient because setting normal forms up to the least weakly Mahlo cardinal needs nontrivial arguments on the constructibility such as Proposition 5.7 and Lemma 7.2 in Rathjen's paper on KPM, while you wrote nothing similar to it. They rarely hold if one just immitates the way of diagonalisation. Since Rathjen's method is very smart and actually necessary, if you have some theoretic reasoning why you succeeded in going beyond weakly Mahlo without applying Rathjen's method, then it is better to write it in order for others to understand. It should be regarded as a great job also for pure mathematics.

Well, I have no counterexample in your definition because I am not fully understanding your description (recall that you have not completed writing the precise definitions of stuffs which I asked above, e.g. Enum, L, and so on). In order to have a precise argument, people need to share the precise definitions. Maybe you are still on the way to write them down. I will read it back after you complete writing. I am looking forward to it.