User blog:12AbBa/12AbBa's hierarchy

12H is a super fast-growing hierarchy.

Defination
\(A_0(n)=n+1 \\ A_{b+1}(n)=A^n_b(n) \\ A_{\alpha}(n)=A^n_{\alpha[n]}(n)\) if and only if \(\alpha\) is a limit ordinal.

Values
\begin{eqnarray*} A_0(n) &=& n+1 \\ A_1(n) &=& 2n \\ A_2(n) &=& 2^nn \\ A_m(n) &>& 2\uparrow^{m-1}n \\ A_{\omega}(n) &>& 2\uparrow^nn \end{eqnarray*}