Hyper Hierarchy

Define Ħ0(n) with the following steps:

-Define a Fast Growing Hierarchy but with \(f_0(n)\) = 1 + 0.0000...001, where there are n 0s after the dot. (F1 hierarchy)

-Define a fast growing hierarchy, but with \(f_0(n)\) = n↑nn (F2 hierarchy)

-Express the F2 hierarchy number \(F2_{\omega}(n)\) in the F1 hierarchy.

-Use the subscript that you now have in the F1 hierarchy number and put it in the F2 hierarchy.

If "a" is a successor, then Ħa(n) = n copies of Ħa-1(n)

If "a" is a limit ordinal, then Ħa(n) = Ħa[n](n)

-If the n is not natural, for example "n,...." then just turn it into simple n.