On the existence of infinite, non-trivial F-sets

© 2016 Elsevier Inc. In this paper we prove a conjecture of J. Andrade, S.J. Miller, K. Pratt and M. Trinh, showing the existence of a non-trivial infinite F-set over F q [x] for every fixed q. We also provide the proof of a refinement of the conjecture, involving the notion of width of an F-set, which is a natural number encoding the complexity of the set.