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Graduate Seminar
Sebastien Vasey Carnegie Mellon University Title: Universal Classes Abstract: Universal classes are a general modeltheoretic framework introduced in the seventies by Saharon Shelah to study certain classes of modules. It encompasses several natural algebraic objects, such as vector spaces and locally finite groups.I will present generalizations to universal classes of several concepts and results of linear algebra. For example, a universal class which has a single model of a "highenough" infinite size has a single model in every highenough size. Moreover, such classes admit an independence notion generalizing linear independence in vector spaces. I will also discuss a more general framework (also due to Shelah), abstract elementary classes, and conjectured extensions of these results there. Date: Tuesday, September 15, 2015 Time: 5:30 pm Location: Wean Hall 8220 Submitted by: Zilin Jiang 