More generally, given any set \(A\), one can build the smallest transitive model of ZF that contains \(A\) and all the ordinals in a similar manner as \(L\), but now starting with the transitive closure of \(\{A \}\), i.e., the smallest transitive set that contains \(A\), instead of \({\varnothing}\). The resulting model, \(L(A)\), need not be however a model of the AC. One very important such model is \(L(\mathbb{R})\), the smallest transitive model of ZF that contains all the ordinals and all the real numbers.