User blog comment:Sait2000/Goodstein Hierarchy/@comment-11227630-20141123034844

I guess $$G_\alpha(n)$$ is approximately $$H_{\varepsilon_0^\alpha}(n)$$ or $$f_{\varepsilon_0\alpha}(n)$$, so "Goodstein Hierarchy" is catched by FGH at $$\varepsilon_0^\omega$$.