An inner model of ZFC is a transitive proper class that contains all the ordinals and satisfies all ZFC axioms. Thus, \(L\) is the smallest inner model, while \(V\) is the largest. Some large cardinals, such as inaccessible, Mahlo, or weakly-compact, may exist in \(L\). That is, if \(\kappa\) has one of these large cardinal properties, then it also has the property in \(L\). But some large cardinals cannot exist in \(L\). Indeed, Scott (1961) showed that if there exists a measurable cardinal \(\kappa\), then \(V\ne L\). It is important to notice that \(\kappa\) does belong to \(L\), since \(L\) contains all ordinals, but it is not measurable in \(L\) because a \(\kappa\)-complete non-principal measure on \(\kappa\) cannot exist there.