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  1. On Modal Logics of Model-Theoretic Relations.Denis I. Saveliev & Ilya B. Shapirovsky - 2020 - Studia Logica 108 (5):989-1017.
    Given a class \ of models, a binary relation \ between models, and a model-theoretic language L, we consider the modal logic and the modal algebra of the theory of \ in L 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 L. We calculate such theories for the submodel and the quotient relations. We prove a downward Löwenheim–Skolem (...)
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  • Interpolation and the Interpretability Logic of PA.Evan Goris - 2006 - Notre Dame Journal of Formal Logic 47 (2):179-195.
    In this paper we will be concerned with the interpretability logic of PA and in particular with the fact that this logic, which is denoted by ILM, does not have the interpolation property. An example for this fact seems to emerge from the fact that ILM cannot express Σ₁-ness. This suggests a way to extend the expressive power of interpretability logic, namely, by an additional operator for Σ₁-ness, which might give us a logic with the interpolation property. We will formulate (...)
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