User blog:Pellucidar12/Attempt at a FGH related notation

This is written as a series of numbers in parentheses separated by commas, for example (x, y, z).

The first number on the left (x) represents the input of a FGH function.

The second number (y) represents the yth function after a limit ordinal

The third number (z) represents the zth limit ordinal (in this case, if z is 0 it is treating 0 as a limit ordinal, even though it's really not one)

So (0, 1, 1) = F1(1)

(1, 1, 1) = fw+1(1)

(2, 2, 2) = fw2+2(2)

You can extend this with a fourth number, making (x, y, z, a), where a equals the ath fixed point after ω, meaning z is the zth limit ordinal after the fixed point defined by a, etc.

For a further extension, you can have (x, y, z, a, b), where b is the bth admissible ordinal after  ω (if b is 0 you just ignore it, if b is 1 then it's the Church-Kleene ordinal, etc.)

This is a very rough prototype though.