I asked this [question](https://math.stackexchange.com/questions/980586/o-minimal-theories-with-non-dense-order-type) on MSE, but I haven't received any comments or responses (also, it has a very low view count), so I thought I would also ask it here. 


In this [paper](http://www.ams.org/journals/tran/1986-295-02/S0002-9947-1986-0833698-1/S0002-9947-1986-0833698-1.pdf), 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 a counterexample. 


Thanks



O-minimal Theories with Non-Dense Order Type
The restriction that the ordering be dense was removed by Pillay and Steinhorn in *Definable Sets in Ordered Structures III*, Trans. Amer. Math. Soc. 309 (1988) 469-476. The abstract of that paper reads: "We show that any o-minimal structure has a strongly o-minimal theory."


