User blog comment:MilkyWay90/My ordinal function/@comment-5529393-20180624012343

lvl(n,n,n) is roughly the Ackermann function, so a0 is about fw in the FGH.

ab+1(n) = F(n,ab(n)) = abn!(n). Iterating a function n! times is a little stronger than one increment of the fast-growing hiearchy, but much weaker than two increments.

So for finite m, am(n) will be between fw+m(n) and fw+m+1(n).

At limit ordinals your hierarchy is a little different because it does the iteration, whereas the FGH does not. So your hierarchy gets an extra increment so:

For b >= w, ab(n) will be between fw+b+1(n) and fw+b+2(n).