MAXIMALITY OF LOGIC WITHOUT IDENTITY

Abstract Lindström’s theorem obviously fails as a characterization of first-order logic without identity ( $\mathcal {L}_{\omega \omega }^{-} $ ). In this note, we provide fix: show that is maximal abstract satisfying weak form the isomorphism property (suitable for identity-free languages and studied in [11]), Löwenheim–Skolem property, compactness. Furthermore, compactness can be replaced by being recursively enumerable validity under certain conditions. proofs, use strong upwards not available framework with identity.