User blog comment:PsiCubed2/A Surjection from the Natural Numbers to the SVO/@comment-25601061-20171218164923/@comment-30754445-20171219184304

I can't find a link at the moment, but I can reconstruct - more or less - a system that follows the same general idea as her original BHO-level notation:

(1) Ord(1) = 0

(2) Ord(2) = 1

(3) Ord(xy) = Ord(x)+Ord(y)

(4) Ord(p2k) = Ω×ω^(Ord(k))

(5) Ord(p2k+1) = ψ(Ord(k))

(6) When your final result is an uncountable ordinal x, replace it with ψ(x).

The above is very similar to Emllightened's original notation, but the minor details might differ.