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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.27816 |
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| _version_ | 1866909004426379264 |
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| author | Nayir, Ebru Özsahakyan, Melissa |
| author_facet | Nayir, Ebru Özsahakyan, Melissa |
| contents | We show that the VC-density in certain theories of oriented abelian groups is at most the size of parameter variables, which yields dp-minimality. We further prove that the VC-density of formulas in pairs of such models is bounded by twice the size of parameter variables. This uniform upper bound is shown to be sharp, and as a consequence, we show that such pairs have dp-rank 2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27816 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | VC-Density in Divisible Oriented Abelian Groups and Their Pairs Nayir, Ebru Özsahakyan, Melissa Logic We show that the VC-density in certain theories of oriented abelian groups is at most the size of parameter variables, which yields dp-minimality. We further prove that the VC-density of formulas in pairs of such models is bounded by twice the size of parameter variables. This uniform upper bound is shown to be sharp, and as a consequence, we show that such pairs have dp-rank 2. |
| title | VC-Density in Divisible Oriented Abelian Groups and Their Pairs |
| topic | Logic |
| url | https://arxiv.org/abs/2604.27816 |