 Heyting algebra

A Heyting algebra is a bounded distributive lattice with an implication $a\Rightarrow b$ characterized by $x\le (a\Rightarrow b)$ exactly when $x\wedge a\le b$.

A Heyting algebra is a specific type of mathematical structure that arises in the field of lattice theory and intuitionistic logic. Heyting algebras generalize Boolean algebras, which are used in classical logic, by accommodating the principles of intuitionistic logic. ### Definition A Heyting algebra is a bounded lattice \( H \) equipped with an implication operation \( \to \) that satisfies certain conditions.