Getting more colors

2009/12/29 by Todd Eisworth, Eisworth, Todd
Mathematics · #03E02 #Advanced Topology and Set Theory #FOS: Mathematics #Limits and Structures in Graph Theory #Logic (math.LO) #Mathematical and Theoretical Analysis #math.LO #msc:03E02

paper · pdf · doi:10.48550/arxiv.0912.5366

Initial version

arxiv created 2009/12/29 · openalex publication_date 2009/12/29 · arxiv updated 2010/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish a coloring theorem for successors of a singular cardinals, and use it prove that for any such cardinal μ, we have μ⁺\nrightarrow[μ⁺]²_μ⁺ if and only if μ⁺\nrightarrow[μ⁺]²_θ for arbitrarily large θ<μ.

Citations

• A note on strong negative partition relations

Related

• A coloring theorem for succesors of singular cardinal
• Successors of singular cardinals and coloring theorems. I
• Colouring of successor of regular again
• Successors of Singular Cardinals and Coloring Theorems II
• On idealized versions of \pr₁(μ⁺,μ⁺,μ⁺,\cf(μ))