1998/01/22 by Mark Hovey, Hovey, Mark, John H. Palmieri +2 · 1 citation
Mathematics · #06D10 #55P42 #55P60 #Algebraic Topology (math.AT) #FOS: Mathematics #Rings, Modules, and Algebras #math.AT #msc:06D10 #msc:55P42 #msc:55P60
paper · pdf · doi:10.48550/arxiv.math/9801103
22 pages
arxiv created 1998/01/22 · openalex publication_date 1998/01/22 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using Ohkawa's theorem that the collection of Bousfield classes is a set, we perform a number of constructions with Bousfield classes. In particular, we describe a greatest lower bound operator; we also note that a certain subset DL of the Bousfield lattice is a frame, and we examine some consequences of this observation. We make several conjectures about the structure of the Bousfield lattice and DL. In particular, we conjecture that DL is obtained by killing "strange" spectra, such as the Brown-Comenetz dual of the sphere. We introduce a new "Boolean algebra of spectra" cBA, which contains Bousfield's BA and is complete. Our conjectures allow us to identify cBA as being isomorphic to the complete atomic Boolean algebra on K(n) : n>= 0, A(n) : n>= 2, and HFp. Our conjectures imply that BA is the subBoolean algebra consisting of finite wedges of the K(n) and A(n), and their complements.