The dp-rank of abelian groups
An equation to compute the dp-rank of any abelian group is given. It is also shown that its dp-rank, or more generally that of any one-based group, agrees with its Vapnik–Chervonenkis density. Furthermore, strong abelian groups are characterised to be precisely those abelian groups A such that there...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/98555 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/98555 |
| Access Level: | acceso abierto |
| Palabra clave: | Abelian group One-based Vc-density Dp-rank Lógica simbólica y matemática (Matemáticas) 1102.10 Teoría de Modelos |
| Sumario: | An equation to compute the dp-rank of any abelian group is given. It is also shown that its dp-rank, or more generally that of any one-based group, agrees with its Vapnik–Chervonenkis density. Furthermore, strong abelian groups are characterised to be precisely those abelian groups A such that there are only finitely many primes p such that the group A/pA is infinite and for every prime p, there are only finitely many natural numbers n such that (p^n A)[p]/(p^{n + 1} A)[p] is infinite. Finally, it is shown that an infinite stable field of finite dp-rank is algebraically closed. |
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