Linear theories of global fields with absolute values
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914422628286464 |
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| author | Fehm, Arno Touchard, Pierre |
| author_facet | Fehm, Arno Touchard, Pierre |
| contents | We study the theory of a global field k as a k-vector space with a predicate for one of the absolute values on k. For example, we prove that in this language a global field with an ultrametric or real archimedean absolute value has a decidable theory, while with a complex absolute value the theory is always undecidable. We also study the existential theories and axiomatize k together with predicates for all non-complex absolute values on k simultaneously. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24720 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Linear theories of global fields with absolute values Fehm, Arno Touchard, Pierre Logic Number Theory 03C60, 12L05, 12L12, 03C10 We study the theory of a global field k as a k-vector space with a predicate for one of the absolute values on k. For example, we prove that in this language a global field with an ultrametric or real archimedean absolute value has a decidable theory, while with a complex absolute value the theory is always undecidable. We also study the existential theories and axiomatize k together with predicates for all non-complex absolute values on k simultaneously. |
| title | Linear theories of global fields with absolute values |
| topic | Logic Number Theory 03C60, 12L05, 12L12, 03C10 |
| url | https://arxiv.org/abs/2603.24720 |