  We develop a model-theoretic framework for the study of distal factors of
strongly ergodic, measure-preserving dynamical systems of countable groups. Our
main result is that all such factors are contained in the (existential)
algebraic closure of the empty set. This allows us to recover some rigidity
results of Ioana and Tucker-Drob as well as prove some new ones: for example,
that strongly ergodic, distal systems are coalescent and that every two such
systems that are weakly equivalent are isomorphic. We also prove the existence
of a universal distal, ergodic system that contains any other distal, ergodic
system of the group as a factor.
