User blog comment:Hyp cos/DAN not into Taranovsky's notation/@comment-32697988-20180707100826/@comment-11227630-20180707112647

See the updated paragraph.

This doesn't mean DAN stronger than TON, because there might be other structures in TON that don't work in DAN ways. For example, C(Ω2,C(Ω22,0)) has similar recursion level as a 2-separator, while C(Ω2+C(Ω2,C(Ω22,0))2,0) corresponds with 1-separator and C(Ω2+C(Ω2,C(Ω22,0))+C(C(Ω22+C(Ω2+C(Ω2,C(Ω22,0))2,0)3,0),C(Ω22,0)),0) corresponds with "0-separator".