It is known that conjugacy classes of elements in orthogonal groups over number fields have a finite width. In this talk, we will present evidence that the same is true for conjugacy classes of elements in higher rank arithmetic groups of orthogonal type. We will show that the question of whether a conjugacy class of such a group has a finite width can be viewed as a congruence subgroup problem on a non-standard saturated model of the group. This is joint work with Nir Avni.