Artifact-centric systems are a recent paradigm for representing and implementing business processes. We present further results on the verification problem of artifact-centric systems specified by means of FO-CTL specifications. While the general problem is known to be undecidable, results in the literature prove decidability for artifact systems with infinite domains under boundedness and conditions such as uniformity. We here follow a different approach and investigate the general case with infinite domains. We show decidability of the model checking problem for the class of artifact-centric systems whose database schemas consist of a single unary relation, and we show that that the problem is undecidable if artifact systems are defined by using one binary relation or two unary relations.