The Ubiquity of Sidon Sets That Are Not $I_0$
  We prove that every infinite, discrete abelian group admits a pair of $I_0$ sets whose union is not $I_0$. In particular, this implies that every such group contains a Sidon set that is not $I_{0}$. 
Kathryn E. Hare and L. Thomas Ramsey
math.CA math.FA