The Ostaszewski square and homogeneous Souslin trees
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- Cite this article as:
- Rinot, A. Isr. J. Math. (2014) 199: 975. doi:10.1007/s11856-013-0065-0
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.
© Hebrew University Magnes Press 2014