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VC-Density in Pairs of Ordered Vector Space
Published 16 May 2024 in math.LO | (2405.10069v2)
Abstract: We show that the VC-density of any partitioned formula in a pair of ordered vector spaces is bounded above by twice the number of parameter variables. We also show that this bound is optimal and, as a by-product, we prove that no dense pair of o-minimal structures is dp-minimal.
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