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Preprint Number 1979

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1979. Kartas Konstantinos
The asymptotic theory of p-adic fields

Submission date: 8 May 2021


We prove that the set of sentences true in all but finitely many finite extensions of 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 𝔽_p((t)) with a predicate for powers of t. This answers a variant of a question of Derakhshan-Macintyre.

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Full text arXiv 2105.03771: pdf, ps.

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