1 results
MAXIMALITY OF LOGIC WITHOUT IDENTITY
- Part of
-
- Journal:
- The Journal of Symbolic Logic / Volume 89 / Issue 1 / March 2024
- Published online by Cambridge University Press:
- 10 January 2023, pp. 147-162
- Print publication:
- March 2024
-
- Article
-
- You have access
- Open access
- HTML
- Export citation
-
Lindström’s theorem obviously fails as a characterization of first-order logic without identity (
$\mathcal {L}_{\omega \omega }^{-} $). In this note, we provide a fix: we show that 
$\mathcal {L}_{\omega \omega }^{-} $ 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.
