论文标题
领域的有限不确定性II：PAC，PRC和PPC领域
Finite Undecidability in Fields II: PAC, PRC and PpC Fields
论文作者
论文摘要
如果$ \ mbox {cons}（σ）$对于每个非空的有限有限的$σ\ subseteq \ mbox {th th}（k; k; \ nathcal {l}）$，则是无环语$ \ MATHCAL {L} $的field $ k $是有限的。我们调整了源自Cherlin-Van Den Dries-Macintyre/Ershov（用于PAC领域）和Haran（对于PRC Fields）的论点，以证明所有PAC和PRC领域都是有限的。我们描述了将证明调整为p $ p $ c字段时出现的困难，并且显示无界的p $ p $ c字段是有限的公理。这项工作来自作者的博士学位论文，是Arxiv：2210.12729的续集。
A field $K$ in a ring language $\mathcal{L}$ is finitely undecidable if $\mbox{Cons}(Σ)$ is undecidable for every nonempty finite $Σ\subseteq \mbox{Th}(K; \mathcal{L})$. We adapt arguments originating with Cherlin-van den Dries-Macintyre/Ershov (for PAC fields) and Haran (for PRC fields) to prove all PAC and PRC fields are finitely undecidable. We describe the difficulties that arise in adapting the proof to P$p$C fields, and show no bounded P$p$C field is finitely axiomatisable. This work is drawn from the author's PhD thesis and is a sequel to arXiv:2210.12729.
