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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
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