The slow-growing hierarchy (SGH) is a certain hierarchy mapping ordinals \(\alpha\) to functions \(g_\alpha: \mathbb{N} ightarrow \mathbb{N}\). Like its name suggests, it grows much slower than its cousins the fast-growing hierarchy and the Hardy hierarchy. The functions are defined as follows: * \(g_0(n) = 0\) * \(g_{\alpha+1}(n) = g_\alpha(n)+1\) * \(g_\alpha(n) = g_{\alpha[n]}(n)\) when \(\alpha\) is a limit ordinal