  Answering a question of Junker and Ziegler, we construct a countable first
order structure which is not omega-categorical, but does not have any proper
non-trivial reducts, in either of two senses (model-theoretic, and
group-theoretic). We also construct a strongly minimal set which is not
omega-categorical but has no proper non-trivial reducts in the model-theoretic
sense.
