Coalgebraic Lindström Theorems
We study modal Lindström theorems from a coalgebraic perspective. We provide three different Lindström theorems for coalgebraic logic, one of which is a direct generalisation of de Rijke's result for Kripke models. Both the other two results are based on the properties of bisimulation invariance, compactness, and a third property: !-bisimilarity, and expressive closure at level !, respectively. These also provide new results in the case of Kripke models. Discussing the relation between our work and a recent result by van Benthem, we give an example showing that only requiring bisimulation invariance together with compactness does not suffice to characterise basic modal logic.
A. Kurz and Y. Venema, "Coalgebraic Lindströom Theorems", Advances in Modal Logic, volume 8, pp. 292-309, August 2010.