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  1. Maximality of Logic Without Identity.Guillermo Badia, Xavier Caicedo & Carles Noguera - 2024 - Journal of Symbolic Logic 89 (1):147-162.
    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 (...)
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  • Alfred Tarski.Mario Gómez-Torrente - 2008 - Stanford Encyclopedia of Philosophy.
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  • Securing Arithmetical Determinacy.Sebastian G. W. Speitel - 2024 - Ergo: An Open Access Journal of Philosophy 11.
    The existence of non-standard models of first-order Peano-Arithmetic (PA) threatens to undermine the claim of the moderate mathematical realist that non-mysterious access to the natural number structure is possible on the basis of our best arithmetical theories. The move to logics stronger than FOL is denied to the moderate realist on the grounds that it merely shifts the indeterminacy “one level up” into the meta-theory by, illegitimately, assuming the determinacy of the notions needed to formulate such logics. This paper argues (...)
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  • One True Logic, by Owen Griffiths and A.C. Paseau.Gil Sagi - 2024 - Mind 133 (532):1220-1229.
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