Lindström Theorems for ∃□-­Bundled Fragment of First­-order Modal Logic

Studies in Logic, Vol. 17, No. 3 (2024): 1–23               PII: 1674­3202(2024)­03­0001­23

Xun Wang

Abstract. In this paper, we provide three different Lindström theorems for ∃□-­bundled fragment of first-­order modal logic, by generalizing de Rijke’s (1995) and van Benthem’s (2007) results for propositional modal logic. All three results are based on the property of bisimulation invariance, and each of them employs another property: compactness, finite depth property, and preservation under ultraproducts over the natural numbers, respectively.