User blog comment:P進大好きbot/Proposal to Choose an Official Standard OCF in This Wiki/@comment-34193315-20191220032726/@comment-28606698-20191220213018

Actually Buchholz’s definition is more elegant and much more powerful than Madore’s one. Once I edited article about Madore’s OCF on Cantor’s Attic (unfortunately now the site doesn’t work) and defined FS for ordinals of this OCF: it requires more rules than for BF or EBF, although Madore’s OCF works only up to ψ(ε_{Ω+1}), meanwhile BF – up to ψ(ε_{Ω_{ω}+1}) and EBF – up to ψ(Λ) with Λ=min{ξ|Ω_ξ=ξ}.

By the way I added comparison between Buchholz’s and Veblen’s functions to make learning of BF easier