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