Erd\H{o}s-Rado Classes

We amalgamate two generalizations of Ramsey’s Theorem–Ramsey classes and the Erd\H{o}s-Rado Theorem–into the notion of a combinatorial Erd\H{o}s-Rado class. These classes are closely related to Erd\H{o}s-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.