Fraïssé limits of metric structures

Itaï Ben Yaacov (1)

1 ICJ - Institut Camille Jordan

We develop \emph{Fraïssé theory}, namely the theory of \emph{Fraïssé classes} and \emph{Fraïssé limits}, in the context of metric structures. We show that a class of finitely generated structures is Fraïssé if and only if it is the age of a separable approximately homogeneous structure, and conversely, that this structure is necessarily the unique limit of the class, and is universal for it. For this purpose, we introduce and use the formalism of \emph{(strictly) approximate isomorphisms}, which has some advantages over the more familiar formalism of finite isomorphisms which one may subsequently modify by a given error term. The use of this formalism naturally gives rise to a natural generalisation of the above, which we call \emph{weak Fraïssé classes}, and whose limits are unique, in a sense, up to arbitrarily small error.

Keywords: Fraïssé class; Fraïssé limit; metric structure; homogeneous structure; perturbation; Gurarij space; Katětov function

Domains: Logic [math.LO]

Itaï Ben Yaacov. Fraïssé limits of metric structures. 2012. ⟨hal-00680898v2⟩