Israel Journal of Mathematics

, Volume 199, Issue 2, pp 975–1012 | Cite as

The Ostaszewski square and homogeneous Souslin trees

  • Assaf Rinot


Assume GCH and let λ denote an uncountable cardinal. We prove that if □λ holds, then this may be witnessed by a coherent sequence 〈C α|α < λ+〉 with the following remarkable guessing property

For every sequence 〈A i | i < λ〉 of unbounded subsets of λ +, and every limit θ < λ, there exists some α < λ + such that otp(C α)=θ and the (i + 1) th -element of C α is a member of A i , for all i < θ.

As an application, we construct a homogeneous λ +-Souslin tree from □λ + CHλ, for every singular cardinal λ.

In addition, as a by-product, a theorem of Farah and Veličković, and a theorem of Abraham, Shelah and Solovay are generalized to cover the case of successors of regulars.


Regular Cardinal Previous Claim Stationary Subset Measure Algebra Maximal Antichain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Hebrew University Magnes Press 2014

Authors and Affiliations

  1. 1.The Center for Advanced Studies in MathematicsBen-Gurion University of the NegevBe’er ShevaIsrael
  2. 2.Department of MathematicsBar-Ilan UniversityRamat-GanIsrael

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