A combinatorial model for the known Bousfield classes

TL;DR

This paper introduces a combinatorial model for the Bousfield classes, providing a structured way to understand their relationships and encapsulate existing results in stable homotopy theory.

Contribution

It constructs an ordered semiring model that captures nearly all known p-local Bousfield classes, unifying and simplifying their study.

Findings

The semiring A models the p-local Bousfield classes.

Most known Bousfield classes are contained in the model.

The model simplifies the understanding of Bousfield class relationships.

Abstract

We give a combinatorial construction of an ordered semiring 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.