Finitely bounded homogeneous structures have finitely bounded Ramsey expansions

A relational structure is homogeneous when every isomorphism between finite substructures extends to an automorphism. It is finitely bounded when its age is defined by finitely many forbidden finite structures, and a Ramsey expansion is an expansion whose age has the Ramsey property.

Bodirsky's Ramsey expansion conjecture. Every finitely bounded homogeneous structure has a finitely bounded Ramsey expansion.

The conjecture is motivated by applications of Ramsey expansions to canonical functions and infinite constraint satisfaction problems. The source presents it as open and notes that current methods generally work with the weaker assumption that a finitely bounded Ramsey expansion is already available.