Diophantine set

In mathematics, a set S of integers is Diophantine precisely if there is some polynomial with integer coefficients f(n,x₁,...,x_k) such that an integer n is in S if and only if there exist some integers x₁,...,x_k with f(n,x₁,...,x_k)=0. (Such a polynomial equation over the integers is also called a Diophantine equation.)

As a consequence of Matiyasevich's theorem, a set of integers is Diophantine if and only if it is recursively enumerable.