 Our next task is to show that L is a model of ZF. A set or a class is transitive if elements of it are also subsets. By a meticulous transfinite induction, Lα  can be shown to be transitive for each α; and therefore so is L itself. This fact, together with the observation that some elementary closure properties hold in L [16]  is enough to show that L is a model of ZF. (Indeed, as it turns out, L is the minimal transitive model of the ZF axioms containing all the ordinals, and is therefore in this sense canonical.)