Know Your Rank!
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866909972426653696 |
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| author | Boissonneau, Blaise Vogel, Lasse |
| author_facet | Boissonneau, Blaise Vogel, Lasse |
| contents | We study definable ranks of ordered fields, ordered abelian groups, and linear orders. For an arbitrary linear order $Γ$, we construct an ordered abelian group $G$ with archimedian spine $Γ$ and an ordered field $K$ with natural value group $G$ such that the definable ranks of $K$, $G$ and $Γ$ are all isomorphic. This answers a question of Krapp, Kuhlmann, and the second author. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18349 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Know Your Rank! Boissonneau, Blaise Vogel, Lasse Logic 03C64, 06F20, 06A05 (primary), 12J15, 12L12, 12J10 (secondary) We study definable ranks of ordered fields, ordered abelian groups, and linear orders. For an arbitrary linear order $Γ$, we construct an ordered abelian group $G$ with archimedian spine $Γ$ and an ordered field $K$ with natural value group $G$ such that the definable ranks of $K$, $G$ and $Γ$ are all isomorphic. This answers a question of Krapp, Kuhlmann, and the second author. |
| title | Know Your Rank! |
| topic | Logic 03C64, 06F20, 06A05 (primary), 12J15, 12L12, 12J10 (secondary) |
| url | https://arxiv.org/abs/2512.18349 |