The intension of a referring expression e in a language is a partial function Ie that assigns to a world w the referent Ie(w) of e there, when there is a referent of e in w. Thus, the intension of "the tallest woman" is a partial function that assigns to w the tallest woman in w.
The intension of a unary predicate P is a partial function IP that assigns to a world w the extension IP(w) of P at w, i.e., the set of all satisfiers of P there.
Intensions are meant to capture the semantic features of terms, with respect to intensional semantics. Now let e be the referring expression:
- The set of even integers.
- is an even integer.
A longshot: Perhaps something like this led Frege to his weird "The concept horse is not a concept" claim.