Submission date: 23 October 2022

Abstract:

A field K in a ring language L is finitely undecidable if Cons(Σ) is undecidable for every nonempty finite Σ ⊆Th(K; L). We extend a construction of Ziegler and use a first-order classification of Anscombe and Jahnke to prove every NIP henselian nontrivially valued field is finitely undecidable. We conclude (assuming the NIP Fields Conjecture) that every NIP field is finitely undecidable.

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Full text arXiv 2210.12729: pdf, ps.