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Talk:Singular cardinals hypothesis

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Two versions

[edit]

Why does the first version of SCH:

SCH1: For all singular strong limit cardinals κ, we have 2κ = κ+.

imply the second version?

SCH2: For all cardinals κ satisfying 2cf(κ) < κ, we have κcf(κ) = κ+

It is clear that the κ in SCH2 must be singular, but not necessarily a strong limit. For example, which instance of SCH1 can be used to show that the configuration , is impossible?

--SCH12 (talk) 09:53, 18 August 2010 (UTC)[reply]