On Ramsey properties of classes with forbidden trees

Abstract

Let F be a set of relational trees and let Forbh(F) be the class of allstructures that admit no homomorphism from any tree in F; all this happens overa fixed finite relational signature $\sigma$. There is a natural way to expandForbh(F) by unary relations to an amalgamation class. This expanded class,enhanced with a linear ordering, has the Ramsey property.Comment: Keywords: forbidden substructure; amalgamation; Ramsey class; partite method v2: changed definition of expanded class; v3: final versio