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  1. On weak square, approachability, the tree property, and failures of SCH in a choiceless context.Arthur W. Apter - 2020 - Mathematical Logic Quarterly 66 (1):115-120.
    We show that the consistency of the theories “ holds below ” + “there is an injection ” + “both and fail” and + “ holds below ” + “there is an injection ” + “ satisfies the tree property” follow from the appropriate supercompactness hypotheses. These provide answers in a choiceless context to certain long‐standing open questions concerning, weak square, approachability, and the tree property. There is nothing special about, and the injection into can be from any ordinal λ (...)
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