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.