May 1
Athar Abdul-Quader,
Purchase College
The Lattice Problem
The lattice problem for models of PA is to determine which lattices can be represented either as lattices of elementary substructures of a model of PA or, more generally, which can be represented as lattices of elementary substructures of a model N that contain a given elementary substructure M of N. In this talk, we will focus on working on particular examples that we hope motivate the main technique (due to Schmerl in 1986) for realizing finite lattices as interstructure lattices. This technique involves representations of lattices as lattices of equivalence relations and the combinatorial properties of such representations.