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Algebra Logika, 2010, Volume 49, Number 3, Pages 346–365 (Mi al443)  

This article is cited in 3 scientific papers (total in 3 papers)

Simple weakly transitive modal algebras

A. V. Karpenkoa, L. L. Maksimovaba

a Novosibirsk State University, Novosibirsk, Russia
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia

Abstract: 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.

Keywords: weakly transitive modal algebra, $DL$-algebra, weakly amalgamable variety, weak interpolation property.

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English version:
Algebra and Logic, 2010, 49:3, 233–245

Bibliographic databases:

UDC: 512.563+510.6+510.5
Received: 07.04.2009
Revised: 01.09.2009

Citation: A. V. Karpenko, L. L. Maksimova, “Simple weakly transitive modal algebras”, Algebra Logika, 49:3 (2010), 346–365; Algebra and Logic, 49:3 (2010), 233–245

Citation in format AMSBIB
\Bibitem{KarMak10}
\by A.~V.~Karpenko, L.~L.~Maksimova
\paper Simple weakly transitive modal algebras
\jour Algebra Logika
\yr 2010
\vol 49
\issue 3
\pages 346--365
\mathnet{http://mi.mathnet.ru/al443}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2766393}
\zmath{https://zbmath.org/?q=an:1255.03060}
\transl
\jour Algebra and Logic
\yr 2010
\vol 49
\issue 3
\pages 233--245
\crossref{https://doi.org/10.1007/s10469-010-9092-7}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77955662750}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. V. Karpenko, “Interpolation properties in the extensions of the logic of inequality”, Siberian Math. J., 51:3 (2010), 439–451  mathnet  crossref  mathscinet  zmath  isi
    2. A. V. Karpenko, “Interpolation in weakly transitive modal logics”, Algebra and Logic, 51:2 (2012), 131–143  mathnet  crossref  mathscinet  zmath  isi
    3. Karpenko A., “Decidability of Some Interpolation Properties For Weakly Transitive Modal Logics”, Larisa Maksimova on Implication, Interpolation, and Definability, Outstanding Contributions to Logic, 15, ed. Odintsov S., Springer, 2018, 171–183  crossref  mathscinet  isi
  • Алгебра и логика Algebra and Logic
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