Heyting algebra
If "H" is a Heyting algebra and "F" is a filter on "H", we define a relation ∼ on "H" as follows: we write whenever and both belong to "F". Then ∼ is an equivalence relation; we write for the quotient set. There is a unique Heyting algebra structure on such that the canonical surjection becomes a Heyting algebra morphism. We call the Heyting algebra the quotient of "H" by "F".