Abstract: 

For expansions of linear orders many different notions of minimality may be considered. Among the most restrictive of these is weak o-minimality while among the least restrictive is dp-minimality, but there are also many other interrelated notions. We expand on machinery introduced by Guingona and Flenner to show that in the context of divisible ordered abelian groups many of these notions coincide. In particular we show that a locally convexly or- derable expansion of a divisible ordered abelian group is weakly o-minimal. This proves the equivalence of several intermediate minimality notions and gives several nice algebraic properties of such structures.

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