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THE STRONG TREE PROPERTY AT SUCCESSORS OF SINGULAR CARDINALS
Published online by Cambridge University Press: 17 April 2014
Abstract
An inaccessible cardinal is strongly compact if, and only if, it satisfies the strong tree property. We prove that if there is a model of ZFC with infinitely many supercompact cardinals, then there is a model of ZFC where ${\aleph _{\omega + 1}}$ has the strong tree property. Moreover, we prove that every successor of a singular limit of strongly compact cardinals has the strong tree property.
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- Copyright © Association for Symbolic Logic 2014
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