old;">L</span>) maps a model
to its maximal
theory, whereas the type embedding function <span
 style="font-family: arial; font-style: italic;">entail</span>(<span
 style="font-weight: bold; font-style: italic;">L</span>) maps an
expression to the theory of all entailed expressions.<br>
<br>
Any collection of models generates a closed theory, whose set of
theorems is the intersection of the theorem sets. Any collection of
expressions generates a closed theory, whose theorem set is the closure
of the theory w