Indiscernibles, EM-types, and Ramsey Classes of Trees
Lynn Scow

TL;DR
This paper extends the class of structures for which indiscernible sets have the modeling property, showing that certain classes of finite trees are Ramsey, by expanding to ordered, locally finite structures that isolate quantifier-free types.
Contribution
It broadens the known class of structures with the modeling property to include ordered, locally finite structures that isolate quantifier-free types, leading to new Ramsey results for finite trees.
Findings
Certain classes of finite trees are Ramsey
Expanded structures still have the modeling property
Generalization from ordered structures to locally finite structures
Abstract
It was shown in \cite{sc12} that for a certain class of structures , -indexed indiscernible sets have the modeling property just in case the age of 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.
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