论文标题
公制结构的近似同构
Approximate Isomorphism of Metric Structures
论文作者
论文摘要
我们给出一种形式主义，以同时概括了本·亚科夫（Ben Yaacov）和本·亚科夫（Ben Yaacov），杜沙（Doucha），尼斯（Nies）和坦科夫（Tsankov）的两篇论文的近似同构，这在很大程度上是不兼容的。这样，我们明确地展示了前一篇论文的扰动系统的Scott句子，例如Banach-Mazur距离和公制空间之间的Lipschitz距离。同时，我们的形式主义是通过扰动系统的轻度概括和某些基本类别的两级结构的语义概括来表征的，这些结构见证了近似同构。作为一个应用程序，我们表明，有限半径的任何$ \ mathbb {r} $ - 树或超级空间的理论稳定，改善了Carlisle和Henson的结果。
We give a formalism for approximate isomorphism in continuous logic simultaneously generalizing those of two papers by Ben Yaacov and by Ben Yaacov, Doucha, Nies, and Tsankov, which are largely incompatible. With this we explicitly exhibit Scott sentences for the perturbation systems of the former paper, such as the Banach-Mazur distance and the Lipschitz distance between metric spaces. Our formalism is simultaneously characterized syntactically by a mild generalization of perturbation systems and semantically by certain elementary classes of two-sorted structures that witness approximate isomorphism. As an application, we show that the theory of any $\mathbb{R}$-tree or ultrametric space of finite radius is stable, improving a result of Carlisle and Henson.
