 In Veldman 1999, an intuitionistic equivalent of the notion of Borel set is formulated, and it is shown that classically equivalent definitions of the Borel sets give rise to a variety of intuitionistically distinct classes, a situation that often occurs in intuitionism. For the intuitionistic Borel sets an analogue of the Borel Hierarchy Theorem is intuitionistically valid. The proof of this fact makes essential use of the continuity axioms discussed above and thereby shows how classical mathematics can guide the search for intuitionistic analogues that, however, have to be proved in a completely different way, sometimes using principles unacceptable from a classical point of view.