User blog:Deedlit11/The slow-growing hierarchy and other hierarchies

You guys are probably familiar with the fast-growing hierarchy:

\begin{eqnarray*} F_0 (n) = n+1 \\ F_{\alpha+1} (n) = F_{\alpha}^n (n)\\ F_{\alpha} (n) = F_{\alpha [n]} (n) \text{ when } \alpha \text{ is a limit ordinal.} \end{eqnarray*}