A set P contained in the positive integers, N, is called predictive if for any zero entropy finite-valued stationary process is measurable with respect to the sigma-field generated by for i in P . The property of having zero entropy is exactly that N is a predictive set. I will discuss some sufficient conditions and a necessary one for a set to be predictive. I will also discuss linear predictivity, predictivity among Gaussian processes and relate these to Riesz sets which arise in harmonic analysis.