User blog comment:Boboris02/Ordinal Analysis of Theories/@comment-11227630-20180213035846/@comment-1605058-20180214113839

Where has Taranovsky defined fundamental sequences for his notation? I know Hyp cos hasdefined one, but not Taranovsky himself.

Either way, totality of \(f_\text{limit of a system}\) is not equivalent to well-foundedness of the system. It is possible to set up a system with fundamental sequences which is not well-founded, but for which the "FGH" is total.