Are there structures $\mathcal{A}$ and $\mathcal{B}$ such that $\mathcal{A}$ and $\mathcal{B}$ are elementary equivalent, not isomorphic but bi-embeddable?



If $\mathcal{A} \equiv \mathcal{B}$ and $\mathcal{A} \not \cong \mathcal{B}$, is it possible that $\mathcal{A}$ and $\mathcal{B}$ are bi-embeddable?
Take the free groups $F\_n$ and $F\_m$ where $m\neq n$ and both are bigger than 1. 
This paper:
<http://www.math.mcgill.ca/olga/p3new.PDF>
proves that they both have the same elementary theory. The groups are not isomorphic, but each one can be embedded in the other.


