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Axiomatic Set Theory: Problem sheet 7 1. Prove that for any infinite cardinal κ, cf (κ) is a regular cardinal. 2. Suppose κ, λ are infinite cardinals such that κ ≥ λ. Prove that if λ ≥ cf (κ), then κλ > κ.
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Document Date: 2009-02-02 11:27:43
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Axiomatic Set Theory: Problem sheet 7 1. Prove that for any infinite cardinal κ, cf (κ) is a regular cardinal. 2. Suppose κ, λ are infinite cardinals such that κ ≥ λ. Prove that if λ ≥ cf (κ), then κλ > κ.