Let L be a countable relational language. Baldwin asked whether there is an ab initio generic L-structure which is superstable but not ω-stable. We give a positive answer to his question, and prove that there is no ab initio generic L-structure which is superstable but not ω-stable, if L is finite and the generic is saturated.

We show that if a class K of finite relational structures is closed under quasi-substructures, then there is no saturated K-generic structure that is superstable but not ω -stable.