In the report of this workshop, it is mentioned that every stable homogeneous structure is interpretable in the dense linear order. I failed to find this result in the papers cited in the report. Does anyone know where can I find a proof of this result?
I should also say that I don't know anything about model theory, which is probably the reason I couldn't find a reference for this result. I will be very happy if someone can point me any reference to this result.
This result is interesting to me because I think it can imply that if we can decide existence of finite solutions of a system of linear equations definable using the dense linear order then we can do the same for a system of linear equations definable using a stable homogeneous structure (the formal definition of definable is definition 4.1 in here)
The result in question is Theorem 3.1 in the following paper:
A.H. Lachlan, Structures coordinatized by indiscernible sets, Annals of Pure and Applied Logic, Volume 34, Issue 3, 1987, Pages 245-273. https://doi.org/10.1016/0168-0072(87)90003-0
The actual theorem stated there is a bit more general and a bit more precise than the quotable consequence that every (countable) stable homogeneous structure is interpretable in $(\mathbb{Q},<)$.
Lachlan proves that if $M$ is a countable structure in a finite language which is $\aleph_0$-categorical and $\aleph_0$-stable and such that every strictly minimal set definable in $M^{eq}$ is indiscernible, then there is an "explicit definition of a structure from a linear ordering" $\mathbb{D}$ such that $M=\mathbb{D}(N)$ for every countable linear order $N$.
At the beginning of the paper, Lachlan notes that the hypothesis holds for every stable homogeneous structure in a finite relational language. And the data of an "explicit definition of a structure from a linear ordering" is not literally an interpretation, but it can be used to cook up an interpretation.