 In Väänänen’s logics it is easy to see why one needs sets of assignments. He has an atomic formula expressing ‘\(x\) is dependent on \(y\)’. How can we interpret this in a structure, for example the structure of natural numbers? It makes no sense at all to ask for example whether 8 is dependent on 37. But if we have a set X of ordered pairs of natural numbers, it does make sense to ask whether in X the first member of each pair is dependent on the second; the answer Yes would mean that there is a function \(f\) such that each pair \((a,b)\) in X has the form \((f(b),b)\). 