omplete' (in $L$) if and only if its set of
| consequences is maximal consistent.  If T is a theory of $L$, with
| $L$ c $L$’ and $L$ =/= $L$’, then T is not a closed theory of $L$’.
| On the other hand, it is easy to see that if $L$’ c $L$, then the
| 'restriction' of a closed theory T to $L$’, in symbols T | $L$’,
| is always a closed theory of $L$’.  T is a 'subtheory' of T’ iff
| T c T’.  If T is a subtheory of T’, then T’ is an 'extension' of T.
|
| A 'set of axioms' of a theory T