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Fraisse classes with simply characterized big Ramsey degrees by Coulson, Rebecca; Dobrinen, Natasha; Patel, Rehana is a scholarly article available to read on EtoBox.

What is Fraisse classes with simply characterized big Ramsey degrees about?

We formulate a property strengthening the Disjoint Amalgamation Property and prove that every Fraisse structure in a finite relational language with relation symbols of arity at most two having this property has finite big Ramsey degrees which have a simple characterization. It follows that any such Fraisse structure admits a big Ramsey structure. Furthermore, we prove indivisibility for every Fraisse structure in an arbitrary finite relational language satisfying this property. This work offers a streamlined and unifying approach to Ramsey theory on some seemingly disparate classes of Fraisse structures. Novelties include a new formulation of coding trees in terms of 1-types over initial segments of the Fraisse structure, and a direct characterization of the degrees without appeal to the standard method of "envelopes".

Author

Coulson, Rebecca; Dobrinen, Natasha; Patel, Rehana

Published

2020

Language

EN