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Successive weakly compact or singular cardinals. (English) Zbl 0926.03069
Summary: It is shown in ZF that if $$\delta<\delta^+<\Omega$$ are such that $$\delta$$ and $$\delta^+$$ are either both weakly compact or singular cardinals and $$\Omega$$ is large enough for putting the core model apparatus into action then there is an inner model with a Woodin cardinal.

MSC:
 3e+55 Large cardinals 3e+45 Inner models, including constructibility, ordinal definability, and core models 3e+35 Consistency and independence results
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References:
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