Some basic thoughts on the cofinalities of Chang structures with an application to forcing

Consider (κ+++,κ++)↠(κ+,κ) where κ is an uncountable regular cardinal. By a result of Shelah's we have cof(X∩κ++)=κ for almost all X⊂κ+++ witnessing this. Here we consider the question if there could be a similar result for X∩κ+. We will discuss some basic facts implying that this cannot hold i...

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Bibliographic Details
Published inMathematical logic quarterly Vol. 67; no. 3; pp. 354 - 358
Main Author Adolf, Dominik T.
Format Journal Article
LanguageEnglish
Published Berlin Wiley Subscription Services, Inc 01.08.2021
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Summary:Consider (κ+++,κ++)↠(κ+,κ) where κ is an uncountable regular cardinal. By a result of Shelah's we have cof(X∩κ++)=κ for almost all X⊂κ+++ witnessing this. Here we consider the question if there could be a similar result for X∩κ+. We will discuss some basic facts implying that this cannot hold in general. We will use these facts to construct an interesting example of a pseudo Prikry forcing, answering a question of Sinapova.
ISSN:0942-5616
1521-3870
DOI:10.1002/malq.202000029