  We study the relations between several notions of dimension for an additive
set, some of which are well-known and some of which are more recent, appearing
for instance in work of Schoen and Shkredov. We obtain bounds for the ratios
between these dimensions by improving an inequality of Lev and Yuster, and we
show that these bounds are asymptotically sharp, using in particular the
existence of large dissociated subsets of $\{0,1\}^n\subset \mathbb{Z}^n$.
