Tag Archives: Fat stationary set

Distributive Aronszajn trees

Posted on April 4, 2017 by Assaf Rinot in categories: Publications, Squares and Diamonds.

Joint work with Ari Meir Brodsky. Abstract.  Ben-David and Shelah proved that if λ is a singular strong-limit cardinal and 2λ=λ+, then ◻λ∗ entails the existence of a λ-distributive λ+-Aronszajn tree. Here, it is proved that the same conclusion remains … Continue reading →

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Chain conditions of products, and weakly compact cardinals

Posted on June 20, 2014 by Assaf Rinot in categories: Partition Relations, Publications.

Abstract.  The history of productivity of the κ-chain condition in partial orders, topological spaces, or Boolean algebras is surveyed, and its connection to the set-theoretic notion of a weakly compact cardinal is highlighted. Then, it is proved that for every … Continue reading →

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The Ostaszewski square, and homogeneous Souslin trees

Posted on May 18, 2011 by Assaf Rinot in categories: Publications, Souslin Hypothesis, Squares and Diamonds.

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⟩ … Continue reading →

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