User blog comment:Hyp cos/Analysis - BEAF, FGH and SGH (part 3)/@comment-1605058-20131029153716/@comment-11227630-20131030061111

If we reach a catching ordinal C(α), then f_{C(α)+1}(n) will change the active point in SGH to Ω. So C(α+1) will change the active point in C(α) to Ω_ω. C(α+ω) will change it into ψ_I(0) and C(α2) will change it into ψ_I( "what's here in C(α)" ). Then C(αω), which means ω nests, will change the active point in C(α) into I. However large the ordinal is, it still works.