Tag Archives: Microscopic Approach

Full Souslin trees at small cardinals

Joint work with Shira Yadai and Zhixing You. Abstract. A κ-tree is full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full κ-Souslin tree may consistently exist. Shelah gave an affirmative … Continue reading

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A microscopic approach to Souslin-tree constructions. Part II

Joint work with Ari Meir Brodsky. Abstract. In Part I of this series, we presented the microscopic approach to Souslin-tree constructions, and argued that all known -based constructions of Souslin trees with various additional properties may be rendered as applications of … Continue reading

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A remark on Schimmerling’s question

Joint work with Ari Meir Brodsky. Abstract. Schimmerling asked whether ◻λ together with GCH entails the existence of a λ+-Souslin tree, for a singular cardinal λ. Here, we provide an affirmative answer under the additional assumption that there exists a … Continue reading

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A microscopic approach to Souslin-tree constructions. Part I

Joint work with Ari Meir Brodsky. Abstract.  We propose a parameterized proxy principle from which κ-Souslin trees with various additional features can be constructed, regardless of the identity of κ. We then introduce the microscopic approach, which is a simple … Continue reading

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Reduced powers of Souslin trees

Joint work with Ari Meir Brodsky. Abstract. We study the relationship between a κ-Souslin tree T and its reduced powers Tθ/U. Previous works addressed this problem from the viewpoint of a single power θ, whereas here, tools are developed … Continue reading

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Forcing and its Applications Retrospective Workshop, April 2015

I gave an invited talk at Forcing and its Applications Retrospective Workshop, Toronto, April 1st, 2015.  Title: A microscopic approach to Souslin trees constructions Abstract: We present an approach to construct κ-Souslin trees that is insensitive to the identity of … Continue reading

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