If \(\kappa\) is a measurable cardinal, then one can construct an \(L\)-like model in which \(\kappa\) is measurable by taking a \(\kappa\)-complete non-principal and normal measure \(U\) on \(\kappa\), and proceeding as in the definition of \(L\), but now using \(U\) as an additional predicate. The resulting model, called \(L[U]\), is an inner model of ZFC in which \(\kappa\) is measurable, and in fact \(\kappa\) is the only measurable cardinal. The model is canonical, in the sense that any other normal measure witnessing the measurability of \(\kappa\) would yield the same model, and has many of the properties of \(L\). For instance, it has a projective well ordering of the reals, and it satisfies the GCH.