 Among the early applications of the Fraenkel-Mostowski method were the result of Mostowski (1938) that one cannot prove from the Comprehension Axiom Schema alone the equivalence of two different definitions of finiteness and of Lindenbaum and Mostowski (1938) that Zermelo's axioms for set theory are not enough to prove the Axiom of Choice, or even just that every infinite set is the disjoint union of two infinite sets.