Strongly Dependent Ordered Abelian Groups and Henselian Fields
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2017
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| _version_ | 1866917631803523072 |
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| author | Halevi, Yatir Hasson, Assaf |
| author_facet | Halevi, Yatir Hasson, Assaf |
| contents | Strongly dependent ordered abelian groups have finite dp-rank. They are precisely those groups with finite spines and $|\{p\text{ prime}:[G:pG]=\infty\}|<\infty$. We apply this to show that if $K$ is a strongly dependent field, then $(K,v)$ is strongly dependent for any henselian valuation $v$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1706_03376 |
| institution | arXiv |
| publishDate | 2017 |
| record_format | arxiv |
| spellingShingle | Strongly Dependent Ordered Abelian Groups and Henselian Fields Halevi, Yatir Hasson, Assaf Logic Group Theory Strongly dependent ordered abelian groups have finite dp-rank. They are precisely those groups with finite spines and $|\{p\text{ prime}:[G:pG]=\infty\}|<\infty$. We apply this to show that if $K$ is a strongly dependent field, then $(K,v)$ is strongly dependent for any henselian valuation $v$. |
| title | Strongly Dependent Ordered Abelian Groups and Henselian Fields |
| topic | Logic Group Theory |
| url | https://arxiv.org/abs/1706.03376 |