Let 
be a set of urelements, and let 
be the superstructure
with 
as its set of individuals. Let 
be a cardinal number. An enlargement 
is 
-saturated provided that it satisfies the following:
For each internal binary relation 
, and each set 
, if 
is contained in the domain of 
and the cardinality of 
is less than 
, then there exists a 
in the range of 
such that if 
, then 
.
If 
is 
-saturated
for some cardinal 
that is greater than or equal to the cardinality of 
, then we just say that 
is saturated. If it is 
-saturated for some cardinal 
that is greater than or equal to the cardinality of 
, then we say it is polysaturated.
Let 
be the set of real numbers, as urelements. Let 
be a cardinal number that is larger than the cardinality
of the power set of 
, and let 
be a 
-saturated enlargement of 
. Let 
be an internal subset of 
, and let 
. Then 
is a closed subset of 
(in the usual topology of the real numbers).
Using saturated enlargements, one may prove the following result in universal algebra:
Let 
be a variety that satisfies the property that for each subvariety 
of 
, and each algebra 
, if 
is generated by its 
-subalgebras, then 
. Then any 
-sum of locally finite algebras is locally finite.
