Do we need models ?
Ordinary model-theoretic semantics assigns objects to individual symbols as their denotations (n-tuples of objects to n-ary predicates, etc.). In truth valuational semantics, truth values are assigned to atomic formulas directly, and not via an assignment of denotations to their constituent expressions. It may be thought that such a semantics would have difficulty with \(\omega\)-inconsistent sets. The authors develop a non- denotational semantics (it is not quite truth valuational in the old sense) which has exactly the power of classical model-theoretic semantics, suggesting that models (and other denotative notions) are semantically unnecessary.
scientific article; zbMATH DE number 4035804