  One can nonetheless study the impact of “reflection principles” of the form of large set axioms. For example, one can add to constructive and intuitionistic set theories  an axiom asserting the existence of inaccessible  sets.[2]   The addition of large set axioms to intuitionistic ZF was first proposed by Friedman and Scedrov (Friedman and Scedrov 1984). One of their aim was to shed light on the corresponding classical notions; another was to study the impact of these principles on metatheoretical properties of the original set theories. Friedman and Scedrov have shown, for example, that the addition of large set axioms does not compromise the validity of the disjunction and numerical existence properties for IZF.