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