## Logic Seminar

James Freitag

UIC

An introduction to better quasi-orders for algebraic applications

**Abstract:**Various finiteness statements across a range of mathematical areas are related to the theory of quasi-orders. These statements are often not recognized as originally coming from finiteness results in the theory of well-quasi-orders, and as a result, complicated combinatorial arguments for the results are often originally developed ad hoc in the various settings. In this talk, we will explain how various results in differential algebra can be proved by using the theory of better quasi-orders. Better quasi-orders are a natural strengthening of the notion of well-quasi-orders, and the class of bqo's is closed under a number of operations which do not preserve the class of wqo's. Among wqo's, all of those found "in nature" have proven to be bqo's. This lecture will attempt to give the audience the necessary tools to decide if bqo theory can be employed to attack a given finiteness problem.

We meet on the first floor or SEO for lunch at noon.

Tuesday February 14, 2017 at 4:00 PM in SEO 427