User blog comment:12AbBa/A Function Part II/@comment-31040770-20190913164047/@comment-39541634-20190915065625

@P-bot

How was it ill-defined?

@12AbBa

To go beyond epsilon-0, you will need to base your notation on some kind of ordinal notation. There really isn't any way to go around this requirement. Just playing around with different array expansion rules isn't going to do the trick (unless you intentionally/unintentionally copy the rules of an already existing notation such as Bird Arrays or SAN).

(this is also one of the reasons that BEAF is ill-defined beyond tetrational arrays. Bowers was not aware of ordinals when he first created his notation, which is precisely why a naive interpertation of pentational arrays is stuck at epsilon-0. It's called a "fixed point" for a reason...)