Weakly transitive modal algebras are studied. It is proved that the class of simple weakly transitive algebras coincides with the class of simple DL-algebras. A full description is given for finitely generated simple DL-algebras together with their embeddings. As a consequence, it is shown that the varieties of weakly transitive algebras and of DL-algebras are not weakly amalgamable, and that modal logics wK4 and DL do not possess the weak interpolation property.
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Supported by RFBR (project No. 09-01-00090a), by the Grants Council (under RF President) for State Aid of Leading Scientific Schools (grant NSh-3606.2010.1), and by the Russian Ministry of Education through the Analytical Departmental Target Program (ADTP) “Development of Scientific Potential of the Higher School of Learning” (project No. 2.1.1/419). (A. V. Karpenko and L. L. Maksimova)
Translated from Algebra i Logika, Vol. 49, No. 3, pp. 346–365, May–June, 2010.
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Karpenko, A.V., Maksimova, L.L. Simple weakly transitive modal algebras. Algebra Logic 49, 233–245 (2010). https://doi.org/10.1007/s10469-010-9092-7
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DOI: https://doi.org/10.1007/s10469-010-9092-7