International audienceIn simply typed \lam-calculus with one ground type the following theorem due to Loader holds. (i) Given the full model \cF over a finite set, %with at least seven elements, the question whether some element f\in\cF is \lam-definable is undecidable. In the \lam-calculus with intersection types based on countably many atoms, the following is proved by Urzyczyn. (ii) It is undecidable whether a type is inhabited. Both statements are major results presented in \cite{Bare2}. We show that (i) and (ii) follow from each other in a natural way, by interpreting intersection types as continuous functions logically related to elements of \cF. From this, and a result by Joly on \lam-definability, we get that \Urz's theorem already holds for intersection types with at most two atoms
