The Theory of Ordered Abelian Groups does not have the Independence Property
The Theory of Ordered Abelian Groups does not have the Independence Property
We prove that no complete theory of ordered abelian groups has the independence property, thus answering a question by B. Poizat. The main tool is a result contained in the doctoral dissertation of Yuri Gurevich and also in P. H. Schmittâs Elementary properties of ordered abelian groups, which basically transforms …