User blog comment:Hyp cos/Analysis - BEAF, FGH and SGH (part 3)/@comment-2033667-20141013055709/@comment-11227630-20141014100739

My logic is,

First Taranovsky's notation works for all ordinals within its range T.

Then define fundamental sequences for ordinals within T.

Then define catching hierarchy up to T.

Problems come: what about catching hierarchy for ordinals beyond T? We need fundamental sequences for them. Then what's fundamental sequences for ordinals beyond T? We need stronger notation for definition.