Indiscernibles, EM-Types, and Ramsey Classes of Trees

Abstract

The author has previously shown that for a certain class of structures $\mathcal{I}$, $\mathcal{I}$-indexed indiscernible sets have the modeling property just in case the age of $\mathcal{I}$ is a Ramsey class. We expand this known class of structures from ordered structures in a finite relational language to ordered, locally finite structures which isolate quantifier-free types by way of quantifier-free formulas. This result is applied to give new proofs that certain classes of trees are Ramsey. To aid this project we develop the logic of EM-types.