I will be speaking at the Special Session on Model Theory at the 2017 AMS Spring Eastern Sectional Meeting on Saturday, May 6, 2017.

**Abstract**: Given an elementary extension of models of Peano Arithmetic (PA), the set of all such that forms a lattice under inclusion. If is an elementary end extension of and , we say is coded in if there is such that . In this talk, I will discuss the relationship between interstructure lattices and coded sets. Recent work by Schmerl determined those collections of subsets of a model which could be coded in a minimal extension; in this talk, we explore the same question for elementary extensions whose interstructure lattices form a finite distributive lattice.