User blog:Ubersketch/Outline for an ordinal notation

h_a(b) is the first fundamental sequence that cannot be created by using s_a(n) on b.
 * s_0(n)=0
 * s_a+1(n)=s_a(n)+1
 * s_a(b)[n]=s_a[n](b) if a is a limit ordinal else:
 * s_a(b)[n]=s_a(b[n])
 * h_0(n)=1
 * h_1(n)=2
 * h_2(n)=3
 * h_w(n)=w+1
 * h_w+1(n)=w2