 One may nevertheless argue that a formula is true in all models only if it is true under all interpretations of the language by appeal to a second-order principle of reflection. This reflection principle makes sure that a formula \(A\) of the language of second-order set theory is true when the quantifiers are taken to range unrestrictedly over the universal domain if, and only if, \(A\) is true when the quantifiers are restricted to some set-sized initial segment of the universe of a certain  sort.[11]  Shapiro (1987) discusses both the set-theoretic principle and its role in the justification of the claim that if a sentence is true in every standard model, then it is true under every interpretation of the language. Unfortunately, second-order reflection takes us beyond the scope of second-order Zermelo-Fraenkel set theory and the axiom of choice (ZFC).