The hypothesis proposed by Cantor that there is no set with a cardinality greater than that of the natural numbers but less than the cardinality of the set of all subsets of the set of natural numbers (the power set of that set). The generalized continuum hypothesis is that the cardinality of any power set of an infinite set is the next highest cardinality after that of the set itself. Gödel proved in 1938 that the continuum hypothesis is consistent with classical set theory; the American mathematician Paul Cohen proved in 1963 that its negation is so too, i.e. the hypothesis is independent of the other axioms.