  A first-order theory has the Schroder-Bernstein property if any two of its
models that are elementarily bi-embeddable are isomorphic. We prove that if a
countable theory T has the Schroder-Bernstein property then it is classifiable
(it is superstable and has NDOP and NOTOP) and satisfies a slightly stronger
condition than nonmultidimensionality, namely: there cannot be a model M of T,
a type p over M, and an automorphism f of M such that for every two distinct
natural numbers i and j, f^i(p) is orthogonal to f^j(p). We also make some
conjectures about how the class of theories with the Schroder-Bernstein
property can be characterized.
