  In this paper we study the property of the Arf good subsemigroups of
$\mathbb{N}^n$, with $n\geq2$. We give a way to compute all the Arf semigroups
with a given collection of multiplicity branches. We also deal with the problem
of determining the Arf closure of a set of vectors and of a good semigroup,
extending the concept of characters of an Arf numerical semigroup to Arf good
semigroups.
