Another proof of a result of Jech and Shelah

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• 作者：Péter Komjáth (1)
  
• 关键词：partially ordered set ; pcf theory ; 03E05
• 刊名：Czechoslovak Mathematical Journal
• 出版年：2013
• 出版时间：September 2013
• 年：2013
• 卷：63
• 期：3
• 页码：577-582
• 全文大小：
• 作者单位：Péter Komjáth (1)
  
  1. R. E?tv?s University, Budapest, Hungary
  
• ISSN：1572-9141

文摘

Shelah’s pcf theory describes a certain structure which must exist if ${\aleph _\omega }$ is strong limit and $2^{\aleph _\omega } > \aleph _{\omega 1} $ holds. Jech and Shelah proved the surprising result that this structure exists in ZFC. They first give a forcing extension in which the structure exists then argue that by some absoluteness results it must exist anyway. We reformulate the statement to the existence of a certain partially ordered set, and then we show by a straightforward, elementary (i.e., non-metamathematical) argument that such partially ordered sets exist.