Definition:Heyting Algebra

Definition

Let $\left({L, \wedge, \vee, \preceq}\right)$ be a lattice.

Then $\left({L, \wedge, \vee, \preceq}\right)$ is a Heyting algebra if and only if:

$(1): \quad \left({L, \wedge, \vee, \preceq}\right)$ is a Brouwerian lattice

$(2): \quad L$ has a smallest element.

Also known as

A Heyting algebra can also be referred to as a Heyting lattice.

Source of Name

This entry was named for Arend Heyting.

Sources

This article incorporates material from Heyting algebra on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.