Israel Journal of Mathematics

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

The Ostaszewski square and homogeneous Souslin trees

Article

Abstract

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

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

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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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