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We discuss deductive databases with one fixed occurrence of a monadic function symbol(successor) per predicate Databases of this kind can be used in a natural way to model simple patterns of events repeated in time, and this is why we term them temporal. Temporal deductive databases are also interesting from a theoretical point of view, because they give rise to infinite least fix-points and infinite query answers. We study complexity properties of finite query answers and define the notion of infinite objects which makes some infinite least fixpoints computable in finite time