2020/11/01 by James Hanson, Hanson, James
Computer Science · Mathematics · #03C35 #03C45 #03C66 #Advanced Algebra and Logic #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis
paper · pdf · doi:10.48550/arxiv.2011.00589
openalex publication_date 2020/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We explore approximate categoricity in the context of distortion systems, introduced in our previous paper, which are a mild generalization of perturbation systems, introduced by Ben Yaacov. We extend Ben Yaacov's Ryll-Nardzewski style characterization of separably approximately categorical theories from the context of perturbation systems to that of distortion systems. We also make progress towards an analog of Morley's theorem for inseparable approximate categoricity, showing that if there is some uncountable cardinal κ such that every model of size κ is 'approximately saturated,' in the appropriate sense, then the same is true for all uncountable cardinalities. Finally we present some examples of these phenomena and highlight an apparent interaction between ordinary separable categoricity and inseparable approximate categoricity.