As a first step in the development of a general theory of set-indexed martingales, we define predictability on a general space with respect to a filtration indexed by a lattice of sets. We prove a characterization of the predictable \(\sigma\)-algebra in terms of adapted and ``left- continuous'' processes without any form of topology for the index set. We then define a stopping set and show that it is a natural generalization of the stopping time; in particular, the predictable \(\sigma\)-algebra can be characterized by various stochastic intervals generated by stopping sets.