Editing Recursively enumerable language (section)

==Closure properties==
Recursively enumerable languages (REL) are [[closure (mathematics)|closed]] under the following operations. That is, if ''L'' and ''P'' are two recursively enumerable languages, then the following languages are recursively enumerable as well:

* the [[Kleene star]] <math>L^*</math> of ''L''
* the [[Concatenation#Concatenation of sets of strings|concatenation]] <math>L \circ P</math> of ''L'' and ''P''
* the [[Union (set theory)|union]] <math>L \cup P</math>
* the [[Intersection (set theory)|intersection]] <math>L \cap P</math>.

Recursively enumerable languages are not closed under [[set difference]] or complementation. The set difference <math>L - P</math> is recursively enumerable if <math>P</math> is recursive.  If <math>L</math> is recursively enumerable, then the complement of <math>L</math> is recursively enumerable [[if and only if]] <math>L</math> is also recursive.