I recently learned that EU characterized by independence and weak ordering is identifiable, but a utility function like: $U(x)=v_1(x)v_2(x)$ is not identifiable.
Does it mean that "cardinal uniqueness = identifiability"? Or cardinal uniqueness implies identifiability but not the other way?
I found the precise definition of "identifiability" parametric function. But for non-parameteric function, what is the precise definition of identifiability?
For example, does the simplest utility function $u(x)$ characterized by weak order and continuity identifiable by its own? (a.k.a does ordinal uniqueness implies identifiability?)