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arXiv · 2405.10069

VC-Density in Pairs of Ordered Vector Space

Ayhan Günaydın·Ebru Nayir
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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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BibTeXRIS

Ayhan Günaydın, Ebru Nayir. 2024-05-16. VC-Density in Pairs of Ordered Vector Space. https://arxiv.org/abs/2405.10069

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