Partitions with independent iterates along IP-sets

We prove a collection of results inspired by Krengel's theorem on the existence of partitions with infinitely many independent iterates in any weakly mixing measure-preserving dynamical system. Our approach avoids Krengel's use of two-fold mixing thereby obtaining stronger results, including characterizations of mild and strong mixing, as well as weak mixing. We also obtain results for non-weakly mixing systems and for more general group actions.