User blog comment:Syst3ms/YAUD/@comment-35470197-20180810233326/@comment-30754445-20180811194801

@Rpakr

"He is not talking about ordinals. At least he does not say so. "

He is talking about ordinals.

The fact that he claims that he doesn't, doesn't change the fact that he is using the exact same symbols we use for ordinals, and he is manipulating these symbols as ordinals, and (implicitly) he is expecting them to behave precisely as ordinals.

He is also using ordinal terms like cofinality and ordinal arithmetic (+,*,^).

And most importantly:

Username5243, when he created his notation, had ordinals in mind. His entire idea is guided on an intuitive understanding of ordinals. So if the "things-that-look-like-ordinals" don't behave like actual ordinals in some way, the odds are that the system presented here would have little in common with the original UNOCF.

Others use ordinal intuition as well, when they analyse UNOCF.

So I'm sorry, but the claim that "these aren't ordinals" doesn't really make much sense. You better hope that these symbols do behave precisely like ordinals, because if they don't than the entire system wouldn't work as Username5243 originally intended.