Such sets are recursively enumerable languages and every recursively enumerable language is the restriction of some such set to a sub-alphabet of "'A " '.
12.
Within the Chomsky hierarchy, the regular languages, the context-free languages, and the recursively enumerable languages are all cones, whereas the context-sensitive languages and the recursive languages are only faithful cones.
13.
These are all proper inclusions, meaning that there exist recursively enumerable languages that are not context-sensitive, context-sensitive languages that are not context-free and context-free languages that are not regular.
