Constructible Universe

In set theory, the constructible universe, also called the Gödel constructible universe and denoted L, is a particular class of sets that can be described entirely in terms of simpler sets, built up as the union of the constructible hierarchy. It was introduced by Kurt Gödel in 1938. Gödel proved that L is an inner model of the Zermelo-Fraenkel axioms, and that both the axiom of choice and the generalized continuum hypothesis hold within it, showing that these statements are consistent with the other axioms of set theory if those axioms are themselves consistent.