Fraïssé limit via forcing

Suppose \mathcal{L} is a finite relational language and \mathcal{K} is a class of finite \mathcal{L}-structures closed under substructures and isomorphisms. It is called aFra\"{i}ss\'{e} class if it satisfies Joint Embedding Property (JEP) and Amalgamation Property (AP). A Fra\"{i}ss\'{e} limit, denoted Flim(\mathcal{K}), of aFra\"{i}ss\'{e} class \mathcal{K} 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 Flim(\mathcal{K})) structure into which every member of \mathcal{K} 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.

کلیدواژه ها:

Fraisse limit ، Focing ، uncountable cardinals