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

Studia Logica 41 (4):415 - 428 (1982)
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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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Filtered subdirect products.Janusz Czelakowski - 1996 - Bulletin of the Section of Logic 24:92-96.

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References found in this work

The mathematics of metamathematics.Helena Rasiowa - 1963 - Warszawa,: Państwowe Wydawn. Naukowe. Edited by Roman Sikorski.
2-element matrices.Wolfgang Rautenberg - 1981 - Studia Logica 40 (4):315 - 353.

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