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Weak covering and the tree property. (English) Zbl 0941.03055
A cardinal \(\delta\) is said to have the tree property if there is no Aronszajn \(\delta\)-tree. Suppose that there is no transitive model of ZFC + “there is a strong cardinal”. Let \(K\) denote the core model. In the paper it is shown that if \(\delta\) has the tree property then \(\delta^{+K} =\delta^+\) and \(\delta\) is weakly compact in \(K\).

MSC:
03E45 Inner models, including constructibility, ordinal definability, and core models
03E55 Large cardinals
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