# Definition:Heyting Algebra

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## 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.*