Undecidability of expansions of Laurent series fields by cyclic discrete subgroups

Leo Gitin

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arXiv · 2408.13900

Undecidability of expansions of Laurent series fields by cyclic discrete subgroups

Leo Gitin

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Abstract

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 $\alpha$ of positive $t$-adic valuation.

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BibTeX RIS

Leo Gitin. 2024-08-25. Undecidability of expansions of Laurent series fields by cyclic discrete subgroups. https://arxiv.org/abs/2408.13900

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