User blog comment:Ikosarakt1/Extensions of Catching function/@comment-11227630-20131120103731/@comment-11227630-20131121015210

So this F-hierarchy suddenly goes wrong. Fω(n)=fC(ω,n)(n), but C(ω,n) is the (1+n)-th catching point of SGH and F-hierarchy. ω is surely below the first catching point, so ωFC(ω,0)(n)>Fω(n).