Constructible universe

In set theory, the constructible universe (or Gödel's constructible universe), denoted by ${\displaystyle L,}$ is a particular class of sets that can be described entirely in terms of simpler sets. ${\displaystyle L}$ is the union of the constructible hierarchy${\displaystyle L_{\alpha }}$. It was introduced by Kurt Gödel in 1938, who proved that the constructible universe is an inner model of ZF set theory, and also that the axiom of choice and the generalized continuum hypothesis are true in the constructible universe. This shows that both propositions are consistent with the basic axioms of set theory, if ZF itself is consistent. Since many other theorems only hold in systems in which one or both of the propositions is true, their consistency is an important result.