Oh how I wish I had math jax on this site.
b(n,m) function:
n and m are non negative integers.
I define b(n,m) in the following recursive way:
b(n,m) = Gamma_m if n = 0
b(n,m) = b(n-1,b(n-1,b(n-1,b(n-1,m)))) if n > 0
Gamma is the gamma in gamma-naught ordinal.
_ is subscript.
The omegaggol is f_{b(10^{100},10^{100})}(10^{100})
^ is exponentiation
_ is subscript
{} denote the range of _ or ^.
Using this definition,