On Limit Amalgamations of Stratififed Spaces

In this article we prove that stratified spaces and other geometric subfamilies satisfy categorical Fra\"iss\'e properties, a matter that might be of interest for both geometers and logicians. As a motivation we show a new example of a stratified pseudomanifold that satisfies the finite oscillation property with respect to a smooth stratified action. Part of this work was presented by the authors at the First Meeting of Logic and Geometry in Bogot\'a, on Sept. 2010.