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The tree property and the failure of the singular cardinal hypothesis at \(\aleph _{\omega ^{2}}\). (English) Zbl 1270.03104

Summary: We show that given \(\omega \) many supercompact cardinals, there is a generic extension in which the tree property holds at \(\aleph _{\omega ^{2}+1}\) and the SCH fails at \(\aleph _{\omega ^{2}}.\)

MSC:

03E55 Large cardinals
03E05 Other combinatorial set theory
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References:

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