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Open questions related to the problem of Birkhoff and Maltsev

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Abstract

The Birkhoff-Maltsev problem asks for a characterization of those lattices each of which is isomorphic to the lattice L(K) of all subquasivarieties for some quasivariety K of algebraic systems. The current status of this problem, which is still open, is discussed. Various unsolved questions that are related to the Birkhoff-Maltsev problem are also considered, including ones that stem from the theory of propositional logics.

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Authors and Affiliations

  1. Department of Mathematics, State University of New York, 12561, New Paltz, NY, USA

    M. E. Adams

  2. Department of Mathematics and Engineering, Harold Washington College, 60601, Chicago, IL, USA

    K. V. adaricheva

  3. Department of Mathematics, University of Puerto Rico, 00681, Mayag Ăźez, PR, USA

    W. Dziobiak

  4. Institute of Mathematics of the Siberian Branch of RAS, Acad. Koptyug prosp. 4, 630090, Novosibirsk, Russia

    A. V. Kravchenko

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  3. W. Dziobiak
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Special issue of Studia Logica: “Algebraic Theory of Quasivarieties” Presented by Ryszard Wójcicki

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Adams, M.E., adaricheva, K.V., Dziobiak, W. et al. Open questions related to the problem of Birkhoff and Maltsev. Stud Logica 78, 357–378 (2004). https://doi.org/10.1007/s11225-005-7378-x

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