 Axiom of constructibility

Every set belongs to some level of the constructible hierarchy. The assertion is $\forall x\exists \alpha (x\in L_{\alpha })$, not that each set is definable without parameters. The constructible universe theorem supplies a relative-consistency model of this assertion from ZFC.

The Axiom of Constructibility, denoted as \( V = L \), is a principle in set theory that asserts that every set can be constructed in a specific hierarchy of sets called "L," which is the class of all constructible sets. This axiom is part of a broader framework known as the von Neumann universe, which organizes sets into levels based on the complexity of their construction.