A Lindström theorem in many-valued modal logic over a finite MTL-chain

We consider a modal language over crisp frames and formulas evaluated on a finite MTL-chain (a linearly ordered commutative integral residuated lattice). We first show that the basic modal abstract logic with constants for the values of the MTL-chain is the maximal abstract logic satisfying Compactness, the Tarski Union Property and strong invariance for bisimulations. Finally, we improve this result by replacing the Tarski Union Property by a relativization property. © 2019 Elsevier B.V.We are grateful to two anonymous referees and the editor of this journal for their numerous and helpful comments. Their help greatly improved the paper. Guillermo Badia is supported by the project I 1923-N25 of the Austrian Science Fund (FWF). Grigory Olkhovikov is supported by Deutsche Forschungsgemeinschaft (DFG), project WA 936/11-1