Let be an algebraically closed field and let be an ideal in , where is a finite set of indeterminates. Let be such that for any in , if every element of vanishes when evaluated if we set each (), then also vanishes. Then lies in for some . Colloquially, the theory of algebraically closed fields is a complete model.
be an algebraically closed field and let 
be an ideal in 
, where 
is a finite set of indeterminates. Let 
be such that for any 
in 
, if every element of 
vanishes when evaluated if we set each (
), then 
also vanishes. Then 
lies in 
for some 
. Colloquially, the theory of algebraically closed fields is a complete model.