Lattices and Coded Sets – AMS Spring Eastern Sectional Meeting

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 \mathcal{M} \prec \mathcal{N} of models of Peano Arithmetic (PA), the set of all \mathcal{K} such that \mathcal{M} \preceq \mathcal{K} \preceq \mathcal{N} forms a lattice under inclusion. If \mathcal{N} is an elementary end extension of \mathcal{M} and X \subseteq \mathcal{M}, we say X is coded in \mathcal{N} if there is Y \in \mathrm{Def}(\mathcal{N} ) such that X = Y \cap M. 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.