# The Theory of Commuting Boolean Algebras

### Catherine Yan

### Courant Institute of Mathematical Sciences

New York University

### Thursday, February 19, 1998

4:00 PM

### Room 102, Bradley Hall

In this talk we propose a definition of commutativity for Boolean subalgebras.
We will concentrate on two cases: atomic Boolean algebras whose theory
can be expressed in terms of commuting equivalence relations, and Boolean
sigma-algebras which is the stochastic analogue of the first case. In each
case, we deal with a pair of commuting Boolean subalgebras, and characterize
such a pair by a structure theorem. We study the properties of lattices
of commuting Boolean algebras, and develop a proof theory for such lattices.