On Ramsey properties of classes with forbidden trees

Details On Ramsey properties of classes with forbidden trees On Ramsey properties of classes with forbidden trees

2011-11-02

arxiv.org/abs/1111.0674v1

Mathematics

Combinatorics

Keywords: forbidden substructure; amalgamation; Ramsey class; partite method

Scientific paper

Let $\F$ be a set of relational trees and let $\Forbh(\F)$ be the class of
all structures that admit no homomorphism from any tree in $\F$; all this
happens over a fixed finite relational signature $\sigma$. There is a natural
way to expand $\Forbh(\F)$ by unary relations to an amalgamation class. This
expanded class, enhanced with a linear ordering, has the Ramsey property.

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