论文标题
在各个有价值的领域中可解释的组上
On groups interpretable in various valued fields
论文作者
论文摘要
我们研究在三个有价值领域的家庭中可以解释的无限组：$ v $ - 米尼马尔，功率界限$ t $ -convex和$ p $ - 封闭的田野。我们表明，每个这样的组$ g $都有无限制的指数，并且如果$ g $是DP-Minimal，那么它是逐句的。 一路上，我们将任何无限解释的组与无限类型的可定义亚组联系起来，这在四种杰出的$ k $中，对一个组中的一组是同构的。 $ \ Mathcal {O} $是估值环。 我们的工作使用并扩展了[11]中开发的技术，以避免消除想象力。
We study infinite groups interpretable in three families of valued fields: $V$-minimal, power bounded $T$-convex, and $p$-adically closed fields. We show that every such group $G$ has unbounded exponent and that if $G$ is dp-minimal then it is abelian-by-finite. Along the way, we associate with any infinite interpretable group an infinite type-definable subgroup which is definably isomorphic to a group in one of four distinguished sorts: the underlying valued field $K$, its residue field $\mathbf{k}$ (when infinite), its value group $Γ$, or $K/\mathcal{O}$, where $\mathcal{O}$ is the valuation ring. Our work uses and extends techniques developed in [11] to circumvent elimination of imaginaries.
