Well-founded recursion

A recursive definition in which the value at a point depends on its predecessor values in a well-founded relation. For a class relation, set-likeness allows the local set recursions to combine into a class function.

An ordinal-valued function strictly increasing along a relation. For a well-founded set relation, or a set-like class relation, the canonical rank is $\rho (y)=\sup \{\rho (x)+1:xRy\}$.