1. Recursively enumerable languages are not closed under set difference or complementation. 2. The complement of the halting language is therefore not recursively enumerable . 3. However, the complement of this set is not recursively enumerable . 4. In total functional programming languages, such as computably enumerable . 5. In this context, enumerable may be used to mean computably enumerable. 6. In this context, enumerable may be used to mean computably enumerable . 7. Every complete recursively enumerable first-order theory is decidable. 8. Assume that the set of all finitely valid sentences is recursively enumerable . 9. It may be shown that unrestricted grammars characterize the recursively enumerable languages. 10. This method is primarily used to construct recursively enumerable sets with particular properties.
