论文标题
字段中的有限不确定性I：NIP字段
Finite Undecidability in Fields I: NIP 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。我们扩展了Ziegler的构造，（除其他结果）使用ANSCOMBE和JAHNKE的一阶分类来证明每个NIP Henselian非试图估值的领域都是有限的。我们得出结论（假设NIP字段猜想）每个NIP场都是有限的。这项工作来自作者的博士学位论文。
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 extend a construction of Ziegler and (among other results) 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. This work is drawn from the author's PhD thesis.
