Abstract
In a paper from 1997, Shelah asked whether Pr1(λ+,λ+,λ+,λ) holds for every inaccessible cardinal λ. Here, we prove that an affirmative answer follows from □(λ+). Furthermore, we establish that for every pair χ<κ of regular uncountable cardinals, □(κ) implies Pr1(κ,κ,κ,χ).
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