User blog comment:Flitri/A new Ordinal based Function on weakening Large Countable Ordinal analogs of Large Cardinal Axioms/@comment-35470197-20190619222721/@comment-25216794-20190620202733

Huh thanks for that. I understand it much better. How does one go about giving/attempting a proof well founded-ness assuming one has a consistent notation? I do think I have a consistent notation as ordinal tuples are completely defined, C is also fully defined along with examples as well as normal forms which are unique for a given ordinal. For example the notation has C[Ω](C[Ω(1)](0)) as the Bachmann-Howard ordinal for which when I sketched a proof of well-foundedness it was wrong since I was using Π-1-1 sentences.