  We show that the complement of the ring of integers in a number field K is
Diophantine. This means the set of ring of integers in K can be written as {t
in K | for all x_1, ..., x_N in K, f(t,x_1, ..., x_N) is not 0}. We will use
global class field theory and generalize the ideas originating from
Koenigsmann's recent result giving a universal first order formula for Z in Q.
