As Zermelo points out (p. 516 of his paper), the WOT establishes a firm foundation for the theory of infinite cardinality; in particular, it shows, he says, that every set (‘for which the totality of its subsets etc. has a sense’) can be considered as a well-ordered set ‘and its power considered as an aleph’. Later work of Hartogs (see Hartogs 1915) showed that, not only does WOT imply COMP as Zermelo shows, but that COMP itself implies WOT, and thus in turn Zermelo's choice principle. Thus, it is not just COMP which is necessary for a reasonable theory of infinite cardinality, but WOT itself. Despite Zermelo's endorsement here, the correctness of the hypothesis that the scale of aleph numbers represents all cardinals (AH, for short) is a more complicated matter, for it involves the claim that every set is actually equivalent to an initial segment of the ordinals, and not just well-orderable. In axiomatic frameworks for sets, therefore, the truth of AH depends very much on which ordinals are present as sets in the system.