## Logic Seminar

Gabriel Conant

Notre Dame

Stability and sparsity in sets of natural numbers

**Abstract:**Stability and sparsity in sets of natural numbers The additive group of integers is a well-studied example of a stable group, whose definable sets can be easily and explicitly described. However, until recently, very little has been known about stable expansions of this group. In this talk, we examine the relationship between model-theoretic stability of expansions of the form (Z,+,0,A), where A is a subset of the natural numbers, and the number theoretic behavior of A with respect to sumsets, asymptotic density, and arithmetic progressions.

Tuesday March 28, 2017 at 4:00 PM in SEO 427