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- W4313897140 abstract "Abstract 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." @default.
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- W4313897140 date "2023-01-10" @default.
- W4313897140 modified "2023-09-26" @default.
- W4313897140 title "MAXIMALITY OF LOGIC WITHOUT IDENTITY" @default.
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- W4313897140 doi "https://doi.org/10.1017/jsl.2023.2" @default.
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