User blog comment:Hyp cos/Fundamental Sequences in Taranovsky's Notation/@comment-40154718-20190917091450/@comment-40154718-20190918075954

"The well-foundedness of TON is equivalent to the existence of an order-preserving injective map from TON to ordinals." :

By "TON" do you mean the set of all the expressions that are syntactically valid in TON and in standard form ?