2020/11/01 by James Hanson, Hanson, James · 1 citation
Computer Science · Mathematics · #03C15 #03C66 #03C75 #Advanced Algebra and Logic #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge
paper · pdf · doi:10.48550/arxiv.2011.00588
openalex publication_date 2020/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ℝ-tree or ultrametric space of finite radius is stable, improving a result of Carlisle and Henson.