  We compute the model-theoretic Grothendieck ring, $K_0(\mathcal{Q})$, of a
dense linear order (DLO) with or without end points, $\mathcal{Q}=(Q,<)$, as a
structure of the signature $\{<\}$, and show that it is a quotient of the
polynomial ring over $\mathbb{Z}$ generated by $\mathbb
N_+\times(Q\sqcup\{-\infty\})$ by an ideal that encodes multiplicative
relations of pairs of generators. As a corollary we obtain that a DLO satisfies
the pigeon hole principle (PHP) for definable subsets and definable bijections
between them--a property that is too strong for many structures.
