Heyting algebra

English dictionary entry

Meanings

noun

A bounded lattice, L, modified to serve as a model for a logical calculus by being equipped with a binary operation called "implies", denoted → (sometimes ⊃ or ⇒), defined such that (a→b)∧a ≤ b and, moreover, that x = a→b is the greatest element such that x∧a ≤ b (in the sense that if c∧a ≤ b then c ≤ a→b).

Heyting algebra Heyting algebras

After Dutch mathematician Arend Heyting, who developed the theory as a way of modelling his intuitionistic logic.

pseudo-Boolean algebra

Heyting prealgebra pseudo-complement relative pseudo-complement residuated lattice

bi-Heyting algebra biHeyting algebra co-Heyting algebra coHeyting algebra complete Heyting algebra

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