O-minimal Theories with Non-Dense Order Type

Question

In this paper, Knight, Pillay, and Steinhorn prove that for any O-minimal structure $\mathfrak{A}$, in which the underlying order types is dense, and if $\mathfrak{B} \equiv \mathfrak{A}$, then $\mathfrak{B}$ is also O-minimal. Is there a counterexample for when the underlying order type is not dense? I haven't been able to construct one.

Thanks

Answer 1

Pillay and Steinhorn extended the result to o-minimal structures of arbitrary order-type in the third paper in the series.