Distinguishing sets of strong recurrence from van der Corput Sets

Abstract: We construct a set of strong recurrence which is not a van der Corput set. This shows that the class of enhanced van der Corput sets is a proper subclass of sets of strong recurrence. In addition, we derive that the class of sets of strong recurrence is not a subclass of van der Corput sets. This answers some questions asked by Bergelson and Lesigne.