Heyting algebra

Summary

A Heyting algebra is a bounded lattice with an implication operation $a \to b$, the largest element whose meet with $a$ lies below $b$. Every Heyting algebra is a distributive lattice, and every Boolean algebra is a Heyting algebra. Heyting algebras are the algebraic models of intuitionistic logic, in the same way that Boolean algebras are the models of classical logic. The open sets of any topological space form a Heyting algebra.