 where \(E'\subseteq \P(\oN)\times\P(\P(\oN)\) is the relation \(rE'X\iff r\in X\). Moreover, second-order logic over \(\mn_1\) is nothing more than first order logic over \(\mn_2\). When this line of thought is taken to its limit we can see that first order logic over the cumulative hierarchy of sets covers higher order logic over any individual level \(V_\alpha\) of the hierarchy. In a sense, first order logic over the cumulative hierarchy of sets is a very very high order logic over \(\mn_1\).