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arXiv · 2105.03771

An undecidability result for the asymptotic theory of $p$-adic fields

Konstantinos Kartas
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Abstract

Fix a prime $p$. We prove that the set of sentences true in all but finitely many finite extensions of $\mathbb{Q}_p$ is undecidable in the language of valued fields with a cross-section. The proof goes via reduction to characteristic $p$, adapting Pheidas' proof of the undecidability of $\mathbb{F}_p(\!(t)\!)$ with a predicate for powers of $t$. This answers a variant of a question of Derakhshan-Macintyre.

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BibTeXRIS

Konstantinos Kartas. 2021-05-08. An undecidability result for the asymptotic theory of $p$-adic fields. https://doi.org/10.1016/j.apal.2022.103203

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