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Open Questions Related to the Problem of Birkhoff and Maltsev

M. E. Adams, K. V. Adaricheva, W. Dziobiak and A. V. Kravchenko
Studia Logica: An International Journal for Symbolic Logic
Vol. 78, No. 1/2, Algebraic Theory of Quasivarieties (Oct. - Nov., 2004), pp. 357-378
Published by: Springer
Stable URL: http://www.jstor.org/stable/20016660
Page Count: 22
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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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