zbMATH — the first resource for mathematics

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:
 3e+45 Inner models, including constructibility, ordinal definability, and core models 3e+55 Large cardinals
Full Text: