Undecidability of expansions of Laurent series fields by cyclic discrete subgroups
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929474148237312 |
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| author | Gitin, Leo |
| author_facet | Gitin, Leo |
| contents | In 1987, Pheidas showed that the field of Laurent series $\mathbb{F}_q((t))$ with a constant for the indeterminate $t$ and a predicate for the natural powers $\{t^n \mid n > 0\}$ of $t$ is existentially undecidable. We show that the same result holds true if $t$ is replaced by any element $α$ of positive $t$-adic valuation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13900 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Undecidability of expansions of Laurent series fields by cyclic discrete subgroups Gitin, Leo Logic Number Theory 03B25, 12L05 (Primary) 11S99, 11U05 (Secondary) In 1987, Pheidas showed that the field of Laurent series $\mathbb{F}_q((t))$ with a constant for the indeterminate $t$ and a predicate for the natural powers $\{t^n \mid n > 0\}$ of $t$ is existentially undecidable. We show that the same result holds true if $t$ is replaced by any element $α$ of positive $t$-adic valuation. |
| title | Undecidability of expansions of Laurent series fields by cyclic discrete subgroups |
| topic | Logic Number Theory 03B25, 12L05 (Primary) 11S99, 11U05 (Secondary) |
| url | https://arxiv.org/abs/2408.13900 |