In this paper we define the notion of -linearity for and discuss interpretability (and noninterpretability) of -linear orders in structures and theories.

The notion of quasi-minimal structures was defined by B. Zil'ber as a natural generalization of minimal structures. Inspired by his work, we study here basic model theoretic properties of quasiminimal structures. Main result is the construction of ω-saturated quasi-minimal models under ω-stability assumption.

We show that is a quasi-minimal torsion-free divisible abelian group. After discussing the axiomatization of the theory of this structure, we present its ω-saturated quasi-minimal model.