 Direct attempts to extend the negative interpretation to analysis fail because the negative translation of the countable axiom of choice is not a theorem of intuitionistic analysis. However, it is consistent with intuitionistic analysis, including Brouwer’s controversial continuity principle, by the functional version of Kleene’s recursive realizability (cf. Section 6.3 below). It follows that intuitionistic mathematics, which can only be expressed by using all the standard logical connectives and quantifiers, is consistent with a faithful translation of classical mathematics avoiding \(\vee\) and \(\exists.\)