A combinatorial model for the known Bousfield classes

Abstract

We give a combinatorial construction of an ordered semiring $\mathcal{A}$, and show that it can be identified with a certain subquotient of the semiring of $p$–local Bousfield classes, containing almost all of the classes that have previously been named and studied. This is a convenient way to encapsulate most of the known results about Bousfield classes.