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.