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Iterated forcing Luzin set Prikry-type forcing Large Cardinals Constructible Universe Sakurai's Bell inequality Ascent Path Uniformization PFA Reduced Power Ramsey theory over partitions countably metacompact xbox weak Kurepa tree specializable Souslin tree ZFC construction Souslin Tree Closed coloring very good scale Distributive tree square Aronszajn tree stationary reflection Monotonically far Whitehead Problem Singular cofinality unbounded function ccc Vanishing levels Singular Density diamond star Knaster Forcing with side conditions Sigma-Prikry 54G20 incompactness Was Ulam right? O-space Intersection model Universal Sequences GMA Shelah's Strong Hypothesis Forcing Axioms Partition relations for trees Postprocessing function Strong coloring perfectly normal Sierpinski's onto mapping principle Nonspecial tree Minimal Walks weak diamond Cohen real Dowker space SNR Diamond C-sequence Absoluteness Entangled linear order Ascending path Uniformly homogeneous Rainbow sets Ineffable cardinal Successor of Singular Cardinal Subadditive Fodor-type reflection HOD Successor of Regular Cardinal Almost-disjoint family Erdos-Hajnal graphs stick Weakly compact cardinal Forcing Antichain Subtle tree property Interval topology on trees Ulam matrix Non-saturation Knaster and friends Ostaszewski square Uniformly coherent b-scale higher Baire space Mandelbrot set AIM forcing square principles Fast club Almost Souslin Respecting tree Singular cardinals combinatorics middle diamond sap Martin's Axiom tensor product graph Well-behaved magma reflection principles Filter reflection Chang's conjecture Club Guessing Chromatic number S-Space Axiom R Partition Relations Erdos Cardinal super-Souslin tree Strongly compact cardinal Prevalent singular cardinals Cardinal function Rock n' Roll club_AD transformations Microscopic Approach Hindman's Theorem Kurepa Hypothesis Analytic sets L-space Almost countably chromatic Hedetniemi's conjecture Dushnik-Miller Reflecting stationary set strongly bounded groups Commutative projection system Precaliber Diamond-sharp Coherent tree P-Ideal Dichotomy Lipschitz reduction Open Access free Boolean algebra weak square Subnormal ideal positive partition relation Parameterized proxy principle approachability ideal Countryman line Commutative cancellative semigroups Foundations Slim tree Strongly Luzin set Square-Brackets Partition Relations Amenable C-sequence Small forcing Poset Greatly Mahlo Jonsson cardinal Rado's conjecture regressive Souslin tree polarized partition relation projective Boolean algebra OCA Diamond for trees Cardinal Invariants Selective Ultrafilter Generalized descriptive set theory PFA(S)[S] full tree Generalized Clubs indecomposable filter stationary hitting nonmeager set Local Club Condensation. Subtle cardinal Fat stationary set Hereditarily Lindelöf space coloring number free Souslin tree
Tag Archives: Microscopic Approach
Full Souslin trees at small cardinals
Joint work with Shira Yadai and Zhixing You. Abstract. A $\kappa$-tree is full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full $\kappa$-Souslin tree may consistently exist. Shelah gave an affirmative … Continue reading
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 $\diamondsuit$-based constructions of Souslin trees with various additional properties may be rendered as applications of … Continue reading
A remark on Schimmerling’s question
Joint work with Ari Meir Brodsky. Abstract. Schimmerling asked whether $\square^*_\lambda$ together with GCH entails the existence of a $\lambda^+$-Souslin tree, for a singular cardinal $\lambda$. Here, we provide an affirmative answer under the additional assumption that there exists a … Continue reading
A microscopic approach to Souslin-tree constructions. Part I
Joint work with Ari Meir Brodsky. Abstract. We propose a parameterized proxy principle from which $\kappa$-Souslin trees with various additional features can be constructed, regardless of the identity of $\kappa$. We then introduce the microscopic approach, which is a simple … Continue reading
Posted in Publications, Souslin Hypothesis
Tagged 03E05, 03E35, 03E65, 05C05, Coherent tree, Diamond, Microscopic Approach, Parameterized proxy principle, Slim tree, Souslin Tree, square, xbox
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Reduced powers of Souslin trees
Joint work with Ari Meir Brodsky. Abstract. We study the relationship between a $\kappa$-Souslin tree $T$ and its reduced powers $T^\theta/\mathcal U$. Previous works addressed this problem from the viewpoint of a single power $\theta$, whereas here, tools are developed … Continue reading
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 $\kappa$-Souslin trees that is insensitive to the identity of … Continue reading
Posted in Invited Talks
Tagged Microscopic Approach, Parameterized proxy principle, Souslin Tree
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