Unstable classes of metric structures

Saharon Shelah, Alexander Usvyatsov

Published 2008-10-03, updated 2019-08-18Version 2

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.