Maximality of logic without identity
Lindström's theorem obviously fails as a characterization of first-order logic without identity
(is a maximal abstract logic satisfying a weak form of the isomorphism property (suitable for
identity-free languages and studied in [11]), the Löwenheim–Skolem property, and
compactness. Furthermore, we show that compactness can be replaced by being recursively
enumerable for validity under certain conditions. In the proofs, we use a form of strong
upwards Löwenheim–Skolem theorem not available in the framework with identity.
(is a maximal abstract logic satisfying a weak form of the isomorphism property (suitable for
identity-free languages and studied in [11]), the Löwenheim–Skolem property, and
compactness. Furthermore, we show that compactness can be replaced by being recursively
enumerable for validity under certain conditions. In the proofs, we use a form of strong
upwards Löwenheim–Skolem theorem not available in the framework with identity.
Lindström’s theorem obviously fails as a characterization of first-order logic without identity ( is a maximal abstract logic satisfying a weak form of the isomorphism property (suitable for identity-free languages and studied in [11]), the Löwenheim–Skolem property, and compactness. Furthermore, we show that compactness can be replaced by being recursively enumerable for validity under certain conditions. In the proofs, we use a form of strong upwards Löwenheim–Skolem theorem not available in the framework with identity.
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