Graduate Student Seminar- Stone duality for Boolean algebras

Date and Time: April 25 (Friday) 1pm - 2pm

Location: Phillips Hall, Room 736

Speaker: Paula de Lima Souza (GWU, Math department)

Title: Stone duality for Boolean algebras

Abstract: Stone duality refers to a correspondence between certain classes of ordered algebraic structures and topological spaces. This is a generalization of Stone's Representation Theorem (1936), due to Marshall Stone,  which states that every Boolean algebra $B$ is isomorphic to the algebra of clopen subsets of a compact Hausdorff totally disconnected space, its Stone space $S(B)$. Concretely, this isomorphism sends every $b  \in B$ to the set of all ultrafilters on $B$ containing $b$. In this talk, we present a detailed proof of the classical duality between Boolean algebras and Stone spaces. We also illustrate an application of this duality in model theory: the Stone space of $n-$types over a theory.

Attendance is required for all graduate students. We look forward to your participation.