论文标题
没有身份的逻辑的最大性
Maximality of logic without identity
论文作者
论文摘要
Lindström定理显然是作为$ \ Mathcal {l} _ {ωΩ}^{ - } $的一阶逻辑而失败的。在此注释中，我们提供了一个解决方案：我们表明$ \ MATHCAL {l} _ {ωΩ}^{ - } $是\ emph {maximal}之间的抽象逻辑中满足同构属性属性弱的属性的弱形式（适用于身份不含身份的语言）（适用于\ cite {casa} rottery {casa}）属性，并构成了loul-im-sk。此外，我们表明可以通过在某些条件下递归枚举的有效性来代替紧凑性。在证据中，我们使用具有标识的框架中不可用的löwenheim-skolem定理形式。
Lindström theorem obviously fails as a characterization of $\mathcal{L}_{ωω}^{-} $, first-order logic without identity. In this note we provide a fix: we show that $\mathcal{L}_{ωω}^{-} $ is \emph{maximal} among abstract logics satisfying a weak form of the isomorphism property (suitable for identity-free languages and studied in \cite{Casa}), 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.
