Axiom of constructibility

Summary

The axiom of constructibility, written $V = L$, says that every set is constructible, that is, every set lies in the constructible universe $L$. It is consistent with ZF when ZF is consistent, and it decides many questions that ZFC leaves open. It implies the axiom of choice and the generalized continuum hypothesis. It is incompatible with large cardinals such as measurable cardinals, so most set theorists do not accept it as true.