 The above properties in fact characterize FO, in the sense that no proper extension of FO can have (certain combinations of) them. This is the content of a celebrated theorem about model-theoretic logics, Lindström’s Theorem, a version of which is given below. For an accessible proof see, for example, Ebbinghaus, Flum, and Thomas (1994). We say that a logic \(L = \FO(Q_1,\ldots,Q_n)\) relativizes if the “converse” of  (16)  holds for each \(Q_i\), i.e., if each \((Q_i){^{\text{rel}}}\) is definable in L.