2025/12/21 by Hans Schoutens, Schoutens, Hans
Computer Science · Mathematics · #Advanced Topology and Set Theory #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO) #Logic, programming, and type systems
paper · doi:10.48550/arxiv.2512.18896
openalex publication_date 2025/12/21 · openalex created_date 2025/12/24 · openalex updated_date 2026/07/28
The category of models of any theory T in any first-order language L has the surprising property that any small category that is elementarily equivalent with it, already embeds in it. The proof uses an abstract argument via ultrapowers, leaving one wonder which concrete categorical axioms, depending on T and L, are responsible for this embedding result. We also propose a first-order logic for which equivalent categories are always elementarily equivalent.