Varieties of three-valued Heyting algebras with a quantifier

Studia Logica 65 (2):181-198 (2000)
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Abstract

This paper is devoted to the study of some subvarieties of the variety Qof Q-Heyting algebras, that is, Heyting algebras with a quantifier. In particular, a deeper investigation is carried out in the variety Q 3 of three-valued Q-Heyting algebras to show that the structure of the lattice of subvarieties of Qis far more complicated that the lattice of subvarieties of Heyting algebras. We determine the simple and subdirectly irreducible algebras in Q 3 and we construct the lattice of subvarieties (Q 3 ) of the variety Q 3

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Citations of this work

Linear Heyting algebras with a quantifier.Laura Rueda - 2001 - Annals of Pure and Applied Logic 108 (1-3):327-343.
Heyting $$\kappa $$-Frames.Hector Freytes & Giuseppe Sergioli - forthcoming - Studia Logica:1-44.

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References found in this work

Algebraic Logic, I. Monadic Boolean Algebras.Paul R. Halmos - 1958 - Journal of Symbolic Logic 23 (2):219-222.
Free q-distributive lattices.Roberto Cignoli - 1996 - Studia Logica 56 (1-2):23 - 29.

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