Arbitrary null-subject constructions are a common property of null- subject languages. Their semantic and syntactic properties have been studied in the Principles and Parameters framework and have been attributed to the assignment of an arbitrary index at the Logical Form as a consequence of their licensing by the interaction of theta and case theory at the level of Deep Structure. In this paper we review the semantic and syntactic properties of arbitrary null-subjects in Greek and we try to analyse these properties in terms of the more general licensing principles of null-subjects and indefiniteness.