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Concerning axiomatizability of the quasivariety generated by a finite Heyting or topological Boolean algebra

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Abstract

In classes of algebras such as lattices, groups, and rings, there are finite algebras which individually generate quasivarieties which are not finitely axiomatizable (see [2], [3], [8]). We show here that this kind of algebras also exist in Heyting algebras as well as in topological Boolean algebras. Moreover, we show that the lattice join of two finitely axiomatizable quasivarieties, each generated by a finite Heyting or topological Boolean algebra, respectively, need not be finitely axiomatizable. Finally, we solve problem 4 asked in Rautenberg [10].

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  1. The Section of Logic Institute of Philosophy and Sociology, Polish Academy of Sciences, Piotrkowska 179, 90-447, Łódź, Poland

    Wlesław Dziobiak

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  1. Wlesław Dziobiak
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Dziobiak, W. Concerning axiomatizability of the quasivariety generated by a finite Heyting or topological Boolean algebra. Stud Logica 41, 415–428 (1982). https://doi.org/10.1007/BF00403339

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  • DOI: https://doi.org/10.1007/BF00403339

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