  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.
