Submission date: 16 July 2018

Abstract:

We compute the model-theoretic Grothendieck ring, K_0(Q), of a dense linear order (DLO) with or without end points, Q=(Q,<), as a structure of the signature { < }, and show that it is a quotient of the polynomial ring over ℤ generated by ℕ_+ × (Q ⊔ { -∞ }) 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.

Mathematics Subject Classification: 03C64, 06A05, 18F30

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Full text arXiv 1807.06097: pdf, ps.