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  1.  3
    On ultrafilter extensions of first-order models and ultrafilter interpretations.Nikolai L. Poliakov & Denis I. Saveliev - 2021 - Archive for Mathematical Logic 60 (5):625-681.
    There exist two known types of ultrafilter extensions of first-order models, both in a certain sense canonical. One of them comes from modal logic and universal algebra, and in fact goes back to Jónsson and Tarski :891–939, 1951; 74:127–162, 1952). Another one The infinity project proceeding, Barcelona, 2012) comes from model theory and algebra of ultrafilters, with ultrafilter extensions of semigroups as its main precursor. By a classical fact of general topology, the space of ultrafilters over a discrete space is (...)
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  2.  19
    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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  3.  1
    Ultrafilter Extensions Do Not Preserve Elementary Equivalence.Denis I. Saveliev & Saharon Shelah - 2019 - Mathematical Logic Quarterly 65 (4):511-516.
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