# 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.