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Graduate Seminar

Sebastien Vasey
Carnegie Mellon University
Title: Universal Classes

Abstract: Universal classes are a general model-theoretic 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 "high-enough" infinite size has a single model in every high-enough 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