Let $\mathcal L^*$ be a family of finite subsets of $\mathbb N_0$ having the following properties. (a). $\{ 0\}, \{ 1\} \in \mathcal L^*$ and all other sets of $\mathcal L^*$ lie in $\mathbb N_{ \ge 2}$. (b). If $L_1, L_2 \in \mathcal L^*$, then the sumset $L_1 + L_2 \in \mathcal L^*$. We show that there is a Dedekind domain $D$ whose system of sets of lengths equals $\mathcal L^*$.
Categories: math.AC