Extension:
In semantics: The things a term is
true of, in some reality
or domain; the range of a
predicate. This then is contrasted with the
intension of a term.
It should be noted that extensions may come to vary: Once there were
many Mohicans; then there was the last of the Mohicans; and then there were no
Mohicans at all.
Also, some extensions of some terms may be
infinite ('natural number', 'real number'),
and if Cantor is right there are  in some sense  infinities of infinitely
many sizes. (See: Set theory)
Another noteworthy point is that the extension of a
predicate or
relation (such as 'is green' or 'loves') is not quite the same sort of
thing as the extension of a name, at least
intuitively.
And variables have no
extension, but their constant substituends do.
Also, it should be noted that, while the extension of a term in the defined sense (whatever things the term stands for, can be used to refer to) seems fairly clear and intuitive, some of its uses in model theory, formal logic and mathematics may be less clear and intuitive, especially if they involve the assumption that extensions invariably are sets or classes (thereby inviting a lot of set theory) or the assumption that the complement of an extension (whatever things the term is not true of) is as unproblematic as the extebsion itself. This last assumption may well be false, e.g. if one speaks of infinities.
