It follows directly from Shelah’s structure theory that if T is a classifiable theory, then the isomorphism type of any model of T is determined by the theory of that model in the language L∞,ω1(d.q.). Leo Harrington asked if one could improve this to the logic L∞,ℵϵ(d.q.) In [S. Shelah, Characterizing an ℵϵ-saturated model of superstable NDOP theories by its L∞,ℵϵ-theory, Israel Journal of Mathematics 140 (2004) 61–111] Shelah gives a partial positive answer, showing that for T a countable superstable NDOP theory, two ℵϵ-saturated models of T are isomorphic if and only if they have the same L∞,ℵϵ(d.q)-theory. We give here a negative answer to the general question by constructing two classifiable theories, each with 2ℵ1 pairwise non-isomorphic models of cardinality ℵ1, which are all L∞,ℵϵ(d.q.)-equivalent, a shallow depth 3 ω-stable theory and a shallow NOTOP depth 1 superstable theory. In the other direction, we show that in the case of an ω-stable depth 2 theory, the L∞,ℵϵ(d.q)-theory is enough to describe the isomorphism type of all models.