Boolean Algebras

Riccardo Marchesin – PhD Student, Trento

Abstract
Originally created by George Boole in the mid-19th Century as a tool for mathematically analyzing logic, Boolean Algebras have since developed into a modern mathematical discipline, with ties to other fields like set theory, topology, and measure theory.
This talk will first introduce the concept of Boolean Algebra and some related notions (filters, ideals and ultrafilters). Then, we will prove Stone’s representation theorem, which classifies Boolean Algebras up to isomorphisms.
Finally, we will discuss some properties (saturation, κ-distributivity) that are related to complete Boolean Algebras.
The seminar corresponds to the final exam of “Set Theory”, a planned course within Riccardo Marchesin’s first year PHD study programme.