 To demonstrate that the addition of this new axiom to the others did not produce contradictions, von Neumann introduced a method of demonstration, called the "method of inner models", which later became an essential instrument in set theory.The second approach to the problem of sets belonging to themselves took as its base the notion of class, and defines a set as a class which belongs to other classes, while a "proper class" is defined as a class which does not belong to other classes.Under the Zermelo–Fraenkel approach, the axioms impede the construction of a set of all sets which do not belong to themselves.