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Partition relations for trees Analytic sets 54G20 Ramsey theory over partitions Kurepa Hypothesis Sierpinski's onto mapping principle ccc Monotonically far Was Ulam right? Slim tree Open Access Countryman line club_AD Weakly compact cardinal Hindman's Theorem square principles transformations Commutative projection system sap Uniformization Vanishing levels Chromatic number Successor of Singular Cardinal xbox S-Space Rado's conjecture free Boolean algebra Dushnik-Miller Ineffable cardinal ZFC construction Ostaszewski square Knaster and friends stick Club Guessing Cardinal Invariants strongly bounded groups Uniformly homogeneous PFA Reflecting stationary set Iterated forcing Generalized Clubs Forcing with side conditions Strongly Luzin set free Souslin tree Singular cofinality Ascending path Microscopic Approach Almost countably chromatic coloring number Cohen real positive partition relation Erdos-Hajnal graphs Souslin Tree Erdos Cardinal GMA Jonsson cardinal specializable Souslin tree approachability ideal Fast club Closed coloring Universal Sequences Forcing Prevalent singular cardinals reflection principles countably metacompact Almost-disjoint family Reduced Power HOD Coherent tree Large Cardinals Hedetniemi's conjecture perfectly normal C-sequence Successor of Regular Cardinal SNR Selective Ultrafilter Dowker space Chang's conjecture Shelah's Strong Hypothesis weak square tensor product graph Constructible Universe Precaliber middle diamond Martin's Axiom incompactness Prikry-type forcing b-scale Subnormal ideal stationary reflection Small forcing Mandelbrot set Interval topology on trees Singular Density Cardinal function Uniformly coherent Greatly Mahlo Diamond-sharp Axiom R Aronszajn tree Diamond weak Kurepa tree Non-saturation super-Souslin tree Subadditive Minimal Walks very good scale Rock n' Roll Filter reflection Sakurai's Bell inequality Forcing Axioms Amenable C-sequence Intersection model Nonspecial tree Parameterized proxy principle Commutative cancellative semigroups unbounded function Poset Local Club Condensation. square Subtle cardinal regressive Souslin tree Respecting tree diamond star nonmeager set Whitehead Problem Strong coloring Fat stationary set Sigma-Prikry O-space Luzin set Well-behaved magma stationary hitting Knaster Ascent Path Foundations AIM forcing Absoluteness indecomposable filter OCA Postprocessing function L-space projective Boolean algebra Square-Brackets Partition Relations polarized partition relation Generalized descriptive set theory Lipschitz reduction full tree Hereditarily Lindelöf space Strongly compact cardinal PFA(S)[S] weak diamond Entangled linear order Subtle tree property Diamond for trees Singular cardinals combinatorics P-Ideal Dichotomy Partition Relations Ulam matrix higher Baire space Rainbow sets Antichain Almost Souslin Distributive tree Fodor-type reflection
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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