Erdős-Rado Classes

Abstract

We amalgamate two generalizations of Ramsey's Theorem--Ramsey classes and the Erdős-Rado Theorem--into the notion of a combinatorial Erdős-Rado class. These classes are closely related to Erdős-Rado classes, which are those from which we can build generalized indiscernibles and blueprints in nonelementary classes, especially Abstract Elementary Classes. We give several examples and some applications.