Mathias forcing and ultrafilters

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• 作者：Janusz Pawlikowski ; Wojciech Stadnicki
• 关键词：Mathias forcing ; Ramsey ultrafilter ; Laver property
• 刊名：Archive for Mathematical Logic
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：55
• 期：7-8
• 页码：857-865
• 全文大小：395 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematical Logic and Foundations
  Mathematics
  Algebra
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0665
• 卷排序：55

文摘

We prove that if the Mathias forcing is followed by a forcing with the Laver Property, then any \(\mathsf {V}\)-\(\mathsf {q}\)-point is isomorphic via a ground model bijection to the canonical \(\mathsf {V}\)-Ramsey ultrafilter added by the Mathias real. This improves a result of Shelah and Spinas (Trans AMS 325:2023–2047, 1999).