2021/06/25 by Juliette Kennedy, Kennedy, Juliette, Jouko Väänánen +2
Computer Science · Mathematics · #03A05 #03C80 #Advanced Algebra and Logic #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #math.LO #msc:03A05 #msc:03C80
paper · pdf · doi:10.48550/arxiv.2106.13506
openalex publication_date 2021/06/25 · arxiv created 2021/07/11 · arxiv updated 2021/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We ask, when is a property of a model a logical property? According to the so-called Tarski-Sher criterion this is the case when the property is preserved by isomorphisms. We relate this to model-theoretic characteristics of abstract logics in which the model class is definable. This results in a graded concept of logicality in the terminology of Sagi. We investigate which characteristics of logics, such as variants of the Löwenheim-Skolem Theorem, Completeness Theorem, and absoluteness, are relevant from the logicality point of view, continuing earlier work by Bonnay, Feferman, and Sagi. We suggest that a logic is the more logical the closer it is to first order logic. We also offer a refinement of the result of McGee that logical properties of models can be expressed in L∞∞ if the expression is allowed to depend on the cardinality of the model, based on replacing L∞∞ by a ``tamer" logic.