Let's consider the following notions: ring, ideal, lattice, formal theory, measure, probability, event. I will show that these notions are very closely related, and how this relation manifests itself in theorems (Stone th, Lebesgue-Caratheodory th, ring spectrum th, compactness th and the axiom of choice). We will exploit Boolean algebras as a "category theory" for that.
If time permits, I will show how Boolean algebras provide basic intuition to help us understand category theory.
Preliminaries: courses in the first two years of BSc and some basic notions of category theory.
Presenter: Kirill Smirnov
Date: February 18, 2019
Venue: room 3248, Faculty of Mathematics and Mechanics, Saint Petersburg State University, Stary Peterhof, Universitetski pr., 28