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