A generalization of Ohkawa's theorem

TL;DR

This paper extends Ohkawa's theorem, originally about spectra, to a broader context of arbitrary combinatorial model categories, showing that their Bousfield equivalence classes form a set.

Contribution

The paper generalizes Ohkawa's theorem from spectra to all combinatorial model categories, broadening its applicability.

Findings

Bousfield equivalence classes form a set in combinatorial model categories

Extension of Ohkawa's theorem beyond spectra

Provides a foundational result for model category theory

Abstract

A theorem due to Ohkawa states that the collection of Bousfield equivalence classes of spectra is a set. We extend this result to arbitrary combinatorial model categories.