Heyting algebra

Meaning

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).

Related

Similar words

• pseudo-Boolean algebra

Narrower meaning words

• Boolean algebra, complete Heyting algebra, finite distributive lattice

Broader meaning words

• distributive lattice, residuated lattice, bicartesian closed category

Origin

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