User blog comment:Hyp cos/Analysis - BEAF, FGH and SGH (part 3)/@comment-10429372-20131101175336/@comment-3427444-20131103123504

The reason why $$\psi_{\Omega_{I+1}}(0) = \Gamma_{I+1}$$ in the definition given in this blog post is because the definition of the $$\psi$$ function contains the (2-variable) $$\varphi$$ function, along with $$\alpha \mapsto \omega^\alpha$$. $$\Gamma_{I+1}$$ is the smallest ordinal that cannot be reached with I, addition and the $$\varphi$$ function.