## Indiscernibles, EM-types, and Ramsey classes of trees.(English)Zbl 1334.03035

Summary: The author has previously shown that for a certain class of structures $$\ell$$, $$\ell$$-indexed indiscernible sets have the modeling property just in case the age of $$\ell$$ 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.

### MSC:

 03C50 Models with special properties (saturated, rigid, etc.) 03C52 Properties of classes of models 05C55 Generalized Ramsey theory

### Keywords:

generalized indiscernibles; Ramsey class; modeling property
Full Text: