Fraïssé limit via forcing

Suppose is a finite relational language and is a class of finite -structures closed under substructures and isomorphisms. It is called a Fra\ {i}ss {e} class if it satisfies Joint Embedding Property (JEP) and Amalgamation Property (AP). A Fra\ {i}ss {e} limit, denoted , of a Fra\ {i}ss {e} class is the unique\footnote{The existence and uniqueness follows from Fra\ {i}ss {e} s theorem, See \cite{hodges}.} countable ultrahomogeneous (every isomorphism of finitely-generated substructures extends to an automorphism of ) structure into which every member of embeds. Given a Fraïssé class K and an infinite cardinal κ, we define a forcing notion which adds a structure of size κ using elements of K, which extends the Fraïssé construction in the case κ=ω.