 Now the defining axioms for abelian groups have three kinds of symbol (apart from punctuation). First there is the logical symbol = with a fixed meaning. Second there are the nonlogical constants, which get their interpretation by being applied to a particular structure; one should group the quantifier symbols with them, because the structure also determines the domain over which the quantifiers range. And third there are the variables \(x, y\) etc. This three-level pattern of symbols allows us to define classes in a second way. Instead of looking for the interpretations of the nonlogical constants that will make a sentence true, we fix the interpretations of the nonlogical constants by choosing a particular structure \(A\), and we look for assignments of elements of \(A\) to variables which will make a given formula true in \(A\).