We define the interpolative fusion T∪∗ of a family (Ti)i∈I of first-order theories over a common reduct T∩, a notion that generalizes many examples of random or generic structures in the model-theoretic literature. When each Ti is model-complete, T∪∗ coincides with the model companion of T∪ =⋃i∈ITi. By obtaining sufficient conditions for the existence of T∪∗, we develop new tools to show that theories of interest have model companions.

中文翻译：

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插值融合

我们定义插值融合吨∪*一个家庭的(吨一世)一世∈一世一阶理论在一个共同的归约上吨∩，这个概念概括了模型理论文献中许多随机或通用结构的例子。当每个吨一世是模型完备的，吨∪*与模型伴侣不谋而合吨∪ =⋃一世∈一世吨一世. 通过获得存在的充分条件吨∪*，我们开发了新的工具来证明感兴趣的理论有模型伴侣。