User blog comment:Ikosarakt1/Extensions of Catching function/@comment-25418284-20131119195520/@comment-5150073-20131119211923

The choice of SGH and FGH was arbitrary, I can also consider it with SGH and HH, HH and FGH (by the way, it can be shown easily that HH reaches SGH at all epsilon ordinals). As for the generalization, can you please clarify it?