Predicate calculus and metatheoretic concepts within a basic theory for the Foundations of Mathematics (Q1901521)

Summary: Some basic concepts of the syntax and semantics of first-order predicate calculus (predicates, propositions, formulae, interpretations, etc.) are introduced into the frame of the basic theories for the Foundations of Mathematics [\textit{E. De Giorgi}, \textit{M. Forti} and \textit{G. Lenzi}, Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat., IX. Ser. Rend. Lincei, Mat. Appl. 5, No. 1, 11-22 (1994; Zbl 0797.03006)]. The ordinary qualities \textit{Qver}, \textit{Qfals} are unable to evaluate all propositions (Theorem 1). Hence new ``metatheoretic objects'', the metaqualities \textit{Mver}, \textit{Mfals}, are introduced to deal with the problem of truth. Being independent of the fundamental relations \textit{Rfond h} [loc. cit.], these metaqualities provide a powerful ``observatory'' giving a truth value to all interpretations of first-order formulae.