2021/03/27 by James Hanson, Hanson, James
Computer Science · Mathematics · #03C57 #03C66 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2103.14957
openalex publication_date 2021/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the context of metric structures introduced by Ben Yaacov, Berenstein, Henson, and Usvyatsov, we exhibit an explicit encoding of metric structures in countable signatures as pure metric spaces in the empty signature, showing that such structures are universal for bi-interpretation among metric structures with positive diameter. This is analogous to the classical encoding of arbitrary discrete structures in finite signatures as graphs, but is stronger in certain ways and weaker in others. There are also certain fine grained topological concerns with no analog in the discrete setting.