Linear Heyting algebras with a quantifier

✍ Scribed by Laura Rueda

• Book ID: 104307087
• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 176 KB
• Volume: 108
• Category: Article
• ISSN: 0168-0072
• DOI: 10.1016/s0168-0072(00)00054-3

✦ Synopsis

A Q-Heyting algebra is an algebra (H ; ∨; ∧; →; ∇; 0; 1) of type (2; 2; 2; 1; 0; 0) such that (H ; ∨; ∧; →; 0; 1) is a Heyting algebra and the unary operation ∇ satisÿes the conditions ∇0=0, a ∧ ∇a = a, ∇(a ∧ ∇b) = ∇a ∧ ∇b and ∇(a ∨ b) = ∇a ∨ ∇b, for any a, b ∈ H . This paper is devoted to the study of the subvariety QHL of linear Q-Heyting algebras. Using Priestley duality we investigate the subdirectly irreducible linear Q-Heyting algebras and, as consequences, we derive some properties of the lattice of subvarieties of QHL and ÿnd equational bases for some of these subvarieties.