## 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:

 3e+55 Large cardinals 300000 Other combinatorial set theory
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### References:

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