2019/06/11 by William Chan, Chan, William · 1 citation
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.1906.04351
openalex publication_date 2019/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
If N is a proper Polish metric space and M is any countable dense submetric space of N, then the Scott rank of N in the natural first order language of metric spaces is countable and in fact at most ω1M + 1, where ω1M is the Church-Kleene ordinal of M (construed as a subset of ω) which is the least ordinal with no presentation on ω computable from M. If N is a rigid Polish metric space and M is any countable dense submetric space, then the Scott rank of N is countable and in fact less than ω1M.