Abstract

We obtain an improvement of some coloring theorems from Eisworth (Fund Math 202:97–123, 2009; Ann Pure Appl Logic 161(10):1216–1243, 2010), Eisworth and Shelah (J Symb Logic 74(4):1287–1309, 2009) for the case where the singular cardinal in question has countable cofinality. As a corollary, we obtain an “idealized” version of the combinatorial principle Pr1(μ +, μ +, μ +, cf(μ)) that maximizes the indecomposability of the associated ideal.