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Complexity of Quasivariety Lattices

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Algebra and Logic Aims and scope

If a quasivariety A of algebraic systems of finite signature satisfies some generalization of a sufficient condition for Q-universality treated by M. E. Adams and W. A. Dziobiak, then, for any at most countable set {Si | i ∈ I} of finite semilattices, the lattice \( {\displaystyle \prod_{i\in I}\mathrm{S}\mathrm{u}\mathrm{b}\left({S}_i\right)} \) is a homomorphic image of some sublattice of a quasivariety lattice Lq(A). Specifically, there exists a subclass K ⊆ A such that the problem of embedding a finite lattice in a lattice Lq(K) of K -quasivarieties is undecidable. This, in particular, implies a recent result of A. M. Nurakunov.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    M. V. Schwidefsky

  2. Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russia

    M. V. Schwidefsky

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Correspondence to M. V. Schwidefsky.

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(M. V. Schwidefsky) The work is supported by Russian Science Foundation (project 14-21-00065).

Translated from Algebra i Logika, Vol. 54, No. 3, pp. 381–398, May-June, 2015.

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Schwidefsky, M.V. Complexity of Quasivariety Lattices. Algebra Logic 54, 245–257 (2015). https://doi.org/10.1007/s10469-015-9344-7

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