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(d) B i ⊆ λ j ( i ) \ sup { λ j ( ν ) : ν < i } , otp B i = λ j ( i ) and B i ∈ M δ i ,j ( B i ) for some j ( B i ) < κ
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(c) A i ⊆ A ∩ δ i , otp A i = µ + i and A i ∈ M δ i
A self contained proof of Shelah's theorem is presented: If μ is a strong limit singular cardinal of uncountable cofinality and 2μ > μ+ then $$\left( {\begin{array}{*{20}c} {\mu ^ + } \\ \mu \\ \end{array} } \right) \to \left( {\begin{array}{*{20}c} {\mu ^ + } \\ {\mu + 1} \\ \end{array} } \right)_{< cf\mu } $$ .
Archive for Mathematical Logic – Springer Journals
Published: Mar 29, 2005
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