Abstract

In this note I present a Lindström theorem characterizing the hybrid logic H(∃) as the most expressive logic having compactness, the Tarski union property, and invariance under quasi-generated substructures. The logic H(∃) is rather interesting, as it mixes the expressive power brought by the availability of world variables with an “almost local” quantification, which gives it a counting ability. However, H(∃) did not receive the same attention as the other logics in the hybrid family, and only quite recently bisimulation-related invariance results were obtained for it by Badia et al. (2023). The Lindström theorem presented here helps clarify further its characteristics and situate better its place among extensions. The result is based on (Lindström, 1973) and employs a strategy different from the one used in recent Lindström theorems for modal and intuitionistic logics, which require a characterization of the logic at issue with respect to some invariance notion derived from bisimulation. For H(∃) the strategy from (Lindström, 1973) arguably provides a better Lindström theorem, as the invariance notion used gives a clearer perspective on the distinguishing capacities of the competing logics.