# Overview >[!info] Definition >$\mathrm{K}$ is the class of *ordinal-definable sets*. >$\mathrm{V}=\mathrm{K}$ abbreviates "Every set is ordinal-definable". **Theorem.** $V=\mathrm{K}$ iff there is a definable well-ordering of $V$. **Theorem**. If ZF is consistent, then so are (i) $\mathrm{ZF}+\mathrm{GCH}+\mathrm{V}=\mathrm{K}+\mathrm{V} \neq \mathrm{L}$; (ii) $\mathrm{ZF}+\mathrm{V}=\mathrm{K}+2^{\aleph_0} \neq \aleph_1$.