 The problem of an adequate axiomatization of set theory was resolved implicitly about twenty years later by Ernst Zermelo and Abraham Fraenkel.Zermelo–Fraenkel set theory provided a series of principles that allowed for the construction of the sets used in the everyday practice of mathematics, but they did not explicitly exclude the possibility of the existence of a set that belongs to itself.In his doctoral thesis of 1925, von Neumann demonstrated two techniques to exclude such sets—the "axiom of foundation" and the notion of "class."