User blog comment:Googleaarex/Tetrational Arrays/@comment-25418284-20130311001458/@comment-5529393-20130312000411

@Googleaarex: I believe FB100Z was wondering if ordinals could be associated with BEAF notation in a way that made extending BEAF easier. He was not claiming that {4, 4, 4, 4} = ω^3 × 4 + ω^2 × 4 + ω × 4 + 4.

@FB100Z  We could make an association like you say, and the simplest notation using ordinals would be the fast-growing hierarchy itself.

If we wanted to make it a little more like BEAF, we could make the ordinals indices of natural number variables. The base and prime numbers would be separate. This could be defined fairly easily, if you define the airplane based on the fundamental sequence of the smallest ordinal index of a nonzero variable.

To BEAFify it even more, one could try to define large airplanes a la the large airplanes of the Extended Array Notation. This may be more trouble than it is worth though, as you wouldn't get an increased growth rate.