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The consistency strength of successive cardinals with the tree property. (English) Zbl 0994.03042
Summary: If \(\omega_n\) has the tree property for all \(2\leq n<\omega\) and \(2^{<\aleph_\omega}= \aleph_\omega\), then for all \(X\in H_{\aleph_\omega}\) and \(n<\omega\), \(M^\sharp_n(X)\) exists.

MSC:
03E45 Inner models, including constructibility, ordinal definability, and core models
03E55 Large cardinals
03E60 Determinacy principles
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