There were attempts at the statement of axioms before Zermelo, both publicly and in private  correspondence.[6]  In particular, Cantor, in correspondence with Hilbert and Dedekind in the late 1890s, had endeavoured to describe some principles of set  existence[7]  which he thought were legitimate, and would not give rise to the construction of what he called ‘inconsistent totalities’, totalities which engender contradictions. (The best known of these totalities were the totality of all ordinals and the totality of all cardinals.) These principles included those of set union and a form of the replacement axiom, as well as principles which seem to guarantee that every cardinal number is an aleph, which we call for short the ‘Aleph Hypothesis (AH)’.