Indiscernibles, EM-types, and Ramsey Classes of Trees

It was shown in \cite{sc12} that for a certain class of structures \(\I\), \(\I\)-indexed indiscernible sets have the modeling property just in case the age of \(\I\) 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. As a corollary, we may conclude that certain classes of finite trees are Ramsey, some previously known. See updated paper for new references.