关于连续结构的扰动
On perturbations of continuous structures
摘要：
我们给出了一个一般的框架处理扰动的类型和结构的连续逻辑，允许指定哪些部分的逻辑可能会受到干扰。我们证明了可分离的，elementarily等价的结构，这是近似$\aleph_0$饱和到任意小的扰动是同构的任意小的扰动（其中的扰动的概念是数据的一部分）。作为一个推论，我们得到了一个完整的理论，其所有的可分离模型是同构的任意小扰动的Ryll-Nardzewski风格的表征。
英文摘要：
We give a general framework for the treatment of perturbations of types and structures in continuous logic, allowing to specify which parts of the logic may be perturbed. We prove that separable, elementarily equivalent structures which are approximately $\aleph_0$-saturated up to arbitrarily small perturbations are isomorphic up to arbitrarily small perturbations (where the notion of perturbation is part of the data). As a corollary, we obtain a Ryll-Nardzewski style characterisation of complete theories all of whose separable models are isomorphic up to arbitrarily small perturbations.
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