Abstract
From large cardinals we obtain the consistency of the existence of a singular cardinal κ of cofinality ω at which the Singular Cardinals Hypothesis fails, there is a bad scale at κ and κ ++ has the tree property. In particular this model has no special κ +-trees.
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The results in this paper are to appear in the Author’s PHD thesis under the direction of James Cummings, to whom the author would like express his gratitude.
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Unger, S. Aronszajn trees and the successors of a singular cardinal. Arch. Math. Logic 52, 483–496 (2013). https://doi.org/10.1007/s00153-013-0326-y
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DOI: https://doi.org/10.1007/s00153-013-0326-y