Abstract
Answering a question of Sakai (Arch Math Logic 52(1–2):29–45, 2013), we show that the existence of an \(\omega _1\)-Erdős cardinal suffices to obtain the consistency of Chang’s Conjecture with \(\square _{\omega _1, 2}\). By a result of Donder (In: Set theory and model theory (Bonn, 1979), volume 872 of lecture notes in mathematics. Springer, Berlin, pp 55–97, 1981) this is best possible. We also give an answer to another question of Sakai relating to the incompatibility of \(\square _{\lambda , 2}\) and \((\lambda ^+, \lambda ) \twoheadrightarrow (\kappa ^+, \kappa )\) for uncountable \(\kappa \).
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Neeman, I., Susice, J. Chang’s Conjecture with \(\square _{\omega _1, 2}\) from an \(\omega _1\)-Erdős cardinal. Arch. Math. Logic 59, 893–904 (2020). https://doi.org/10.1007/s00153-020-00723-w
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DOI: https://doi.org/10.1007/s00153-020-00723-w