Let be a superstructure
monomorphism, with
and for . Then is an enlargement of provided that for each set in ,
there is a hyperfinite set that contains all the standard entities of .
It is the case that
is an enlargement of
if and only if every concurrent binary relation satisfies the following: There is an element of the range of such that for every in the domain of , the pair is in the relation .
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be a set of urelements, and let 
be the superstructure
with individuals in 
:
,
,
.
be a superstructure
monomorphism, with 
and 
for 
. Then 
is an enlargement of 
provided that for each set 
in 
,
there is a hyperfinite set 
that contains all the standard entities of 
.
is an enlargement of 
if and only if every concurrent binary relation 
satisfies the following: There is an element 
of the range of 
such that for every 
in the domain of 
, the pair 
is in the relation 
.
