  In 1969, Choquet-Bruhat and Geroch established the existence of a unique
maximal globally hyperbolic Cauchy development of given initial data for the
Einstein equations. Their proof, however, has the unsatisfactory feature that
it relies crucially on the axiom of choice in the form of Zorn's lemma. In this
paper we present a proof that avoids the use of Zorn's lemma. In particular, we
provide an explicit construction of this maximal globally hyperbolic
development.
