2006/04/08 by Paolo Lipparini, Lipparini, Paolo
Computer Science · Mathematics · #03E04 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras #math.LO #msc:03E04
paper · pdf · doi:10.48550/arxiv.math/0604191
8 pages
arxiv created 2006/04/08 · openalex publication_date 2006/04/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the decomposability spectrum KD=\λ≥ ω| D is λ-decomposable\ of an ultrafilter D, and show that Shelah's \pcf theory influences the possible values KD can take. For example, we show that if \aaa is a set of regular cardinals, μ∈ \pcfa, the ultrafilter D is |\aaa |+-complete and KD ⊆ \aaa, then μ∈ KD. As a consequence, we show that if λ is singular and for some λ' < λ KD contains all regular cardinals in [λ', λ) then: (a) if \cf λ= ω then either λ∈ KD, or λ+ ∈ KD; and (b) if D is (\cf λ)+-complete then λ+ ∈ KD, and \pp (λ)= λ+.