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