User blog comment:Hyp cos/Fundamental Sequences in Taranovsky's Notation/@comment-40154718-20190917091450/@comment-35470197-20190918092652

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

Right. To be more precise, I meant the set of all standard terms in the main system of Taranovsky's notation. In general, a totally ordered set (S,<) is well-founded if and only if there exists an order-preserving injective map S→α for some ordinal α.