Consider the expansion TS of a theory T by a predicate for a submodel of a reduct T0 of T. We present a setup in which this expansion admits a model companion TS. We show that some of the nice features of the theory T transfer to TS. In particular, we study conditions for which this expansion preserves the NSOP1-ness, the simplicity or the stability of the starting theory T. We give concrete examples of new NSOP1 not simple theories obtained by this process, among them the expansion of a perfect ω-free PAC field of positive characteristic by generic additive subgroups, and the expansion of an algebraically closed field of any characteristic by a generic multiplicative subgroup.

中文翻译：

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归约的一般展开

考虑扩展吨小号一个理论的吨通过归约子模型的谓词吨0的吨. 我们提出了一个设置，其中这个扩展允许一个模型伴侣吨小号. 我们展示了该理论的一些不错的特征吨传送到吨小号. 特别是，我们研究了这种扩展保留国家标准作业程序1-ness，起始理论的简单性或稳定性吨. 我们给出了新的具体例子国家标准作业程序1通过这个过程获得的不是简单的理论，其中包括一个完美的扩展ω-自由的PAC由一般加性子群组成的正特征域，以及代数闭域的扩展任何由一个通用的乘法子群来表征。