5 messages mentioned Hyting-algebras. Never heard of them.Lawvere & Schanuel do not mention them in the 1997 book. Will store the terms for future reference.
Nowadays when I hear "Never heard of x" my subconscious seems to turn it into "never heard of Wikipedia." When five people tell you x is the answer to your question, merely filing it "for future reference" misses the point of the answer. (As one of the five, my examples consisted of the finite nonempty chains and the finite Boolean algebras, which I pointed out to Peter gave an example of every finite positive cardinality, and two for the powers of two. My mistake was to lump these examples together under the common rubric of "Heyting algebra," which appears to have made what was meant to be a simple answer incomprehensible.) As Bill points out, a Heyting algebra is almost the same thing as a CCC in the case of categories that are posets. This is exactly the case when there are finitely many objects (a case where Heyting algebras and distributive lattices are "the same thing" in the sense that they have the same underlying posets), and is close to true modulo existence of joins in the infinite case. In particular a Heyting algebra needs the empty join 0 in order to define negation as x->0, whence the negative integers made a category with its standard ordering is cartesian closed but is not a Heyting algebra for want of a least negative integer. More generally Heyting algebras are required to have all finite joins, not a requirement for posetal cartesian closed categories. Vaughan Pratt