Unstable classes of metric structures

2008/10/03 by Saharon Shelah, Shelah, Saharon, Alexander Usvyatsov +1
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.0810.0734

openalex publication_date 2008/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a strong non-structure theorem for a class of metric structures with an unstable pair of formulae. As a consequence, we show that weak categoricity (that is, categoricity up to isomorphisms and not isometries) implies several versions of stability. This is the first step in the direction of the investigation of weak categoricity and weak stability of metric classes.

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