User blog comment:Flitri/A new Ordinal based Function on weakening Large Countable Ordinal analogs of Large Cardinal Axioms/@comment-35470197-20190619222721/@comment-35470197-20190620223811

Unfortunately, you do not have a consistent notation, and hence it is impossible to prove statements abouve it. Maybe I do not have to pick up what are errors any more.

You need to start with creating a consistent notation. For this purpose, you need to understand ordinals. In order to do so, you need to fix wrong definitions and wrong statements without proofs on ordinals. Only after that, you can prove something about your original stuffs.