A coloring theorem for succesors of singular cardinal

2009/12/31 by Todd Eisworth, Eisworth, Todd
Mathematics · #03E02 #FOS: Mathematics #Logic (math.LO) #math.LO #msc:03E02

paper · pdf · doi:10.48550/arxiv.1001.0194

Initial version

arxiv created 2009/12/31 · arxiv updated 2010/01/14

Abstract

We formulate and prove (in \sf ZFC) a strong coloring theorem which holds at successors of singular cardinals, and use it to answer several questions concerning Shelah's principle Pr₁(μ⁺,μ⁺,μ⁺,\cf(μ)) for singular μ.

Related

• Getting more colors
• 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))