Suppose we have a structure with a given domain and some given relations of various arities, say \(\langle \bD, \bR_1, \ldots, \bR_n\rangle\). And suppose we have a first-order language formed in the usual way, with relation symbols, \(R_1\), …, \(R_n\) whose arities match those of the given relations. We will generally use the typographical convention that \(\bR\) is a relation and \(R\) is the associated formal symbol interpreted by that relation. In the usual way we can build up a first-order language that talks about the structure, where atomic formulas involve \(R_1\), …, \(R_n\) and \(=\). Constants can be simulated by the use of unary relations that are true of single things. For example, in arithmetic we can have a relation \(\bZ\) such that \(\bZ(x)\) holds only when \(x=0\). In the interests of readability, in such a case we would act as if we had a constant symbol in our language that was interpreted by 0. Such informal simplifications make formula reading a bit easier, while nothing significant is lost.