Zorn emigrated to the U.S. and was appointed a Sterling Fellow at Yale University. While at Yale, Zorn wrote his paper "A Remark on Method in Transfinite Algebra" that stated his Maximum Principle, later called Zorn's lemma. It requires a set that contains the union of any chain of subsets to have one chain not contained in any other, called the maximal element. He illustrated the principle with applications in ring theory and field extensions. Zorn's lemma is an alternative expression of the axiom of choice, and thus a subject of interest in axiomatic set theory.