Abstract
Remember that the lattice \(\mathop{\mathrm{L_{q}}}\nolimits (\mathcal{K})\) of all subquasivarieties of a quasivariety \(\mathcal{K}\) is dually algebraic and join semidistributive. The goal of this section is to characterize the completely join irreducible quasivarieties in \(\mathop{\mathrm{L_{q}}}\nolimits (\mathcal{K})\). Most of the results in this section can be found in Section 5.1 of Gorbunov’s book [77].
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Hyndman, J., Nation, J.B. (2018). Structure of Lattices of Subquasivarieties. In: The Lattice of Subquasivarieties of a Locally Finite Quasivariety. CMS Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-78235-5_2
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