Fra\"iss\'e limits of metric structures
Logic
2014-09-09 v4
Abstract
We develop \emph{Fra\"iss\'e theory}, namely the theory of \emph{Fra\"iss\'e classes} and \emph{Fra\"iss\'e limits}, in the context of metric structures. We show that a class of finitely generated structures is Fra\"iss\'e 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. We do this in a somewhat new approach, in which ''finite maps up to errors'' are coded by \emph{approximate isometries}.
Cite
@article{arxiv.1203.4459,
title = {Fra\"iss\'e limits of metric structures},
author = {Itaï Ben Yaacov},
journal= {arXiv preprint arXiv:1203.4459},
year = {2014}
}