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 uniquefootnote{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.