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).
Bibliographical noteFunding Information:
The first author is partially supported by the European Research Council (grant agreement ERC-2018-StG 802756 ) and by the Israel Science Foundation (grant agreement 2066/18 ). The second author is supported by the Foreign Postdoctoral Fellowship Program of the Israel Academy of Sciences and Humanities and by the Israel Science Foundation (grant agreement 2066/18 ).
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