User blog comment:Hyp cos/Fundamental Sequences in Taranovsky's Notation/@comment-40154718-20190916083849/@comment-40154718-20190916091108

I know that TON is an ordinal notation, but I thought that TON expressions represent ordinals,  for example Ω_1 represents the least uncountable ordinals, whose cofinality is itself, doesn't it ? If TON expressions represent ordinals, then TON perhaps is not really but can be associated with the set of all ordinals that can be represented by a TON expression, and that set can be identified with an ordinal which measures the power of TON.