In theories of divisible oriented abelian groups, VC-density is at most the number of parameters (yielding dp-minimality); in pairs of models it is at most twice that, the bound is sharp, and the pairs have dp-rank 2.
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VC-Density in Divisible Oriented Abelian Groups and Their Pairs
In theories of divisible oriented abelian groups, VC-density is at most the number of parameters (yielding dp-minimality); in pairs of models it is at most twice that, the bound is sharp, and the pairs have dp-rank 2.