In this talk, we’ll discuss the remarkable result by A. Khovanskii (1992) concerning the \(n\)-fold sum of additive sets in abelian groups. Specifically, the theorem states that if \(A\) is an additive set in an abelian group \(G\) and we define \(f_A(n)\) as \(\vert nA\vert\) for each \(n\in \mathbb{N}\), then there exists \(n_A\in \mathbb{N}\) and a polynomial \(p_A(x)\in \mathbb{Z}[x]\) such that \(f_A(n)=p_A(n)\) for \(n>n_A\). Additionally, we’ll explore some illustrative examples and discuss open questions related to this result.