 The atomic formulas of second-order logic are defined from terms as follows: If t and \(t'\) are terms, then \(t = t'\) is an atomic formula. If R is an n-ary relation symbol and \(t_1,\ldots,t_n\) are terms, then \(R(t_1,\ldots,t_n)\) is an atomic formula. If X is an n-ary relation variable, then also \(X(t_1,\ldots,t_n)\) is an atomic formula. The intuitive meaning of \(X(t_1,\ldots,t_n)\) is that the elements \(t_1,\ldots, t_n\) are in the relation X or are predicated by X. We do not allow atomic formulas of the form \(X = Y\), although they would have an obvious meaning. We achieve the same effect by using quantifiers.