Axiom of constructibility

The axiom of constructibility is a possible axiom for set theory in mathematics that asserts that every set is constructible. The axiom is usually written as V = L, where V and L denote the von Neumann universe and the constructible universe, respectively. The axiom, first investigated by Kurt Gödel, is inconsistent with the proposition that zero sharp exists and stronger large cardinal axioms (see List of large cardinal properties). Generalizations of this axiom are explored in inner model theory.