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  1. Some characterization and preservation theorems in modal logic.Tin Perkov - 2012 - Annals of Pure and Applied Logic 163 (12):1928-1939.
    A class of Kripke models is modally definable if there is a set of modal formulas such that the class consists exactly of models on which every formula from that set is globally true. In this paper, a class is also considered definable if there is a set of formulas such that it consists exactly of models in which every formula from that set is satisfiable. The notion of modal definability is then generalized by combining these two. For thus obtained (...)
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  • Ultrafilter Extensions of Bounded Graphs are Elementary.Zalán Molnár - forthcoming - Studia Logica:1-23.
    The main motivation of this paper is the study of first-order model theoretic properties of structures having their roots in modal logic. We will focus on the connections between ultrafilter extensions and ultrapowers. We show that certain structures (called bounded graphs) are elementary substructures of their ultrafilter extensions, moreover their modal logics coincide.
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  • Existential definability of modal frame classes.Tin Perkov & Luka Mikec - 2020 - Mathematical Logic Quarterly 66 (3):316-325.
    We prove an existential analogue of the Goldblatt‐Thomason Theorem which characterizes modal definability of elementary classes of Kripke frames using closure under model theoretic constructions. The less known version of the Goldblatt‐Thomason Theorem gives general conditions, without the assumption of first‐order definability, but uses non‐standard constructions and algebraic semantics. We present a non‐algebraic proof of this result and we prove an analogous characterization for an alternative notion of modal definability, in which a class is defined by formulas which are satisfiable (...)
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