A Heyting field is one of the inequivalent ways in constructive mathematics to capture the classical notion of a field. It is essentially a field with an apartness relation. A commutative ring is a Heyting field if ¬, either or is invertible for every , and each noninvertible element is zero. The first two conditions say that the ring is local; the first and third conditions say that it is a field in the classical sense. The prototypical Heyting field is the real numbers.