Two pre-sets are extensionally equivalent if every element of the first family is extensionally equivalent to some element of the second family and vice-versa.
Function equivalence is defined so that
f ~ g iff
∀ x y, x ~ y → f x ~ g y. This extends to equivalence of n-ary
A set function is "definable" if it is the image of some n-ary pre-set function. This isn't exactly definability, but is useful as a sufficient condition for functions that have a computable image.