Abstract(s) :
(Anglais) Let G be a model of Presburger arithmetic. Let L be an expansion of the language of Presburger L_Pres. In this paper, we prove that the
L-theory of G is L_Pres-minimal iff it has the exchange property and is definably complete (i.e., any bounded definable set has a maximum). If the L-theory of G has the exchange but is not definably complete, there is a proper definable convex subgroup H. Assuming that the induced
theories on H and G/H are definable complete and o-minimal resp., we prove that any definable set of G is L_PresU{H}-definable