论文标题
通过密集的亚组扩展O最小理论的同伴表征
Companionability Characterization for the Expansion of an O-minimal Theory by a Dense Subgroup
论文作者
论文摘要
本文为当通过挑选一个可划分的致密和codense子组的一般谓词扩展完整的O最小理论时提供了完整的表征。该结果是由有关模型伴侣存在的最新著作中引入的标准和问题的动机，以及传递到模型伴侣时的一些新稳定性能的保存结果。本文的重点是在O最低设置中建立同伴分隔线，因为这使我们能够提供完整的几何表征。包括示例，其中谓词是一个添加剂亚组，又是一个乘法亚组。本文以简短的讨论对新稳定性的特性和示例进行了简要讨论，这些属性说明了缺乏保存（从“基础” O最低理论到我们定义的扩展的模型伴侣），例如强，nip和ntp $ _2 $，尽管也有一些或所有这些属性所具有的示例。
This paper provides a full characterization for when the expansion of a complete o-minimal theory by a unary predicate that picks out a divisible dense and codense subgroup has a model companion. This result is motivated by criteria and questions introduced in the recent works concerning the existence of model companions, as well as preservation results for some neostability properties when passing to the model companion. The focus of this paper is establishing the companionability dividing line in the o-minimal setting because this allows us to provide a full and geometric characterization. Examples are included both in which the predicate is an additive subgroup, and where it is a multiplicative subgroup. The paper concludes with a brief discussion of neostability properties and examples that illustrate the lack of preservation (from the "base" o-minimal theory to the model companion of the expansion we define) for properties such as strong, NIP, and NTP$_2$, though there are also examples for which some or all three of those properties hold.
