All recursive languages are also recursively enumerable. The unrestricted grammars characterize the recursively enumerable languages. The halting language is therefore recursively enumerable. This method is primarily used to construct recursively enumerable sets with particular properties. It is evident that Diophantine sets are recursively enumerable. Every complete recursively enumerable first-order theory is decidable. Recursively enumerable languages are not closed under set difference or complementation. It is possible to construct languages which are not even recursively enumerable, however. Some pairs of recursively enumerable sets are effectively separable and some are not. In computational complexity theory, the complexity class containing all recursively enumerable sets is RE. Any "axiomatizable" fuzzy theory is recursively enumerable. The class of all recursively enumerable languages is called RE. Later research dealt also with numberings of other classes like classes of recursively enumerable sets. The C preprocessor preprocesses the header files, including and further preprocessing them recursively. Recurrence relations are equations which define one or more sequences recursively.