2019/08/01 by William Chan, Ruiyuan Chen, Chan, William +1
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1908.00179
openalex publication_date 2019/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
An analog of Nadel's effective bound for the continuous Scott rank of metric structures, developed by Ben Yaacov, Doucha, Nies, and Tsankov, will be established: Let \mathscrL be a language of continuous logic with code \mathscrL. Let Ω be a weak modulus of uniform continuity with code Ω. Let D be a countable \mathscrL-pre-structure. Let D denote the completion structure of D. Then SRΩ(D) ≤ ω1^\mathscrL⊕Ω\oplusD, the Church-Kleene ordinal relative to \mathscrL⊕Ω\oplusD.