 Recursive presentation of a group

A recursive presentation has an effectively enumerable alphabet of generators and a recursively enumerable set of relators. Usually the alphabet is finite; when it is countably infinite this is specified explicitly. Enumerating finite products of conjugates of relators and their inverses enumerates all null words. Conversely the enumerable null words can themselves serve as the relators. Recursive presentability does not imply a soluble word problem for a group.