Geodesic
Cardinality reduction theorem for logics ${\mathrm{QHC}}$ and ${\mathrm{QH4}}$
Algebra i logika, Tome 61 (2022) no. 6, pp. 720-741

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The joint logic of problems and propositions ${\mathrm{QHC}}$ introduced by S. A. Melikhov, as well as intuitionistic modal logic ${\mathrm{QH4}}$, is studied. An immersion of these logics into classical first-order predicate logic is considered. An analog of the Löwenheim–Skolem theorem on the existence of countable elementary submodels for ${\mathrm{QHC}}$ and ${\mathrm{QH4}}$ is established.
Keywords: nonclassical logics, Kripke semantics, translation. 
@article{AL_2022_61_6_a4,
     author = {A. A. Onoprienko},
     title = {Cardinality reduction theorem for logics ${\mathrm{QHC}}$ and ${\mathrm{QH4}}$},
     journal = {Algebra i logika},
     pages = {720--741},
     publisher = {mathdoc},
     volume = {61},
     number = {6},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2022_61_6_a4/}
}
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A. A. Onoprienko. Cardinality reduction theorem for logics ${\mathrm{QHC}}$ and ${\mathrm{QH4}}$. Algebra i logika, Tome 61 (2022) no. 6, pp. 720-741. http://geodesic.mathdoc.fr/item/AL_2022_61_6_a4/