User blog comment:Hyp cos/TON, stable ordinals, and my array notation/@comment-31580368-20191006023842/@comment-11227630-20191009084100

Taranovsky has proposed a canonicity on assignment of expressions. In the assignment, some terms correspond with ordinals above their order types (Ω1 is the first one). The assignment is for analysis of the notation, and compared with the structure in some theories. However, canonicity is unambiguous, and it is easy to skip structures in theories.