LATTICES AND BOOLEAN ALGEBRA

Catalog description

In the first part of the course, we study partial orders and view lattices both as partial orders and as algebraic structures. We study some basic constructions involving sublattices, products of lattices, and homomorphic images of lattices. In the second part of the course, we study Boolean algebras, with an aim to proving several representation theorems: first, a representation theorem for finite Boolean algebras, and toward the end of the course, the famous Stone Representation Theorem. We end the course with a look at the connection between classical mereology (or the theory of parthood) and complete Boolean algebras