1 research outputs found
On modal logics of model-theoretic relations
Given a class of models, a binary relation
between models, and a model-theoretic language , we consider the modal logic
and the modal algebra of the theory of in where the modal
operator is interpreted via . We discuss how modal theories of
and depend on the model-theoretic language, their
Kripke completeness, and expressibility of the modality inside . We
calculate such theories for the submodel and the quotient relations. We prove a
downward L\"owenheim--Skolem theorem for first-order language expanded with the
modal operator for the extension relation between models