 The truth definition involves the concepts “for some \(P \subseteq M^n\)” and “for some \(f:M^n \to M\)”. Since we assume set theory as our metalanguage, we can interpret these in the sense of set theory. Thus we interpret “for some \(P \subseteq M^n\)” as “for some set \(P \subseteq M^n\)” and “for some \(f:M^n\to M\)” as “for some set which is a function \(f:M^n\to M\)”.