On modal logics of model-theoretic relations [article]

Denis I. Saveliev, Ilya B. Shapirovsky
2019 arXiv   pre-print
Given a class C of models, a binary relation R between models, and a model-theoretic language L, we consider the modal logic and the modal algebra of the theory of C in L where the modal operator is interpreted via R. We discuss how modal theories of C and R depend on the model-theoretic language, their Kripke completeness, and expressibility of the modality inside L. We calculate such theories for the submodel and the quotient relations. We prove a downward Löwenheim–Skolem theorem for
more » ... der language expanded with the modal operator for the extension relation between models.
arXiv:1804.09810v4 fatcat:4ta7oth5zbdsblofpzdihiw6wy