 The games described in this section adapt almost trivially to many-sorted logic: for example the quantifier \(\forall x_{\sigma}\), where \(x_{\sigma}\) is a variable of sort \(\sigma\), is an instruction for player \(\forall\) to choose an element of sort \(\sigma\). This immediately gives us the corresponding games for second-order logic, if we think of the elements of a structure as one sort, the sets of elements as a second sort, the binary relations as a third and so on. It follows that we have, quite routinely, game rules for most generalised quantifiers too; we can find them by first translating the generalised quantifiers into second-order logic.