Submission date: 25 December 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 adapt arguments originating with Cherlin-van den Dries-Macintyre/Ershov (for PAC fields), Haran (for PRC fields), and Efrat (for PpC fields) to prove all PAC, PRC, and (bounded) PpC fields are finitely undecidable. This work is drawn from the author's PhD thesis and is a sequel to arXiv:2210.12729.

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Full text arXiv 2212.12918: pdf, ps.