Abstract
Let S denote the variety of Sugihara algebras. We prove that the lattice Λ (K) of subquasivarieties of a given quasivariety K \( \subseteq \) S is finite if and only if K is generated by a finite set of finite algebras. This settles a conjecture by Tokarz [6]. We also show that the lattice Λ (S) is not modular.
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Blok, W.J., Dziobiak, W. On the lattice of quasivarieties of Sugihara algebras. Stud Logica 45, 275–280 (1986). https://doi.org/10.1007/BF00375898
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DOI: https://doi.org/10.1007/BF00375898