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Erdos Cardinal Uniformization very good scale regressive Souslin tree Singular Density ccc Commutative cancellative semigroups square principles Universal Sequences L-space Reduced Power perfectly normal Mandelbrot set Ramsey theory over partitions Precaliber Rock n' Roll sap weak Kurepa tree Aronszajn tree Selective Ultrafilter Cardinal Invariants Singular cardinals combinatorics Forcing Axioms SNR Subtle cardinal Ineffable cardinal Distributive tree countably metacompact Lipschitz reduction Rainbow sets Successor of Singular Cardinal Coherent tree approachability ideal Hedetniemi's conjecture Strongly Luzin set PFA(S)[S] C-sequence Absoluteness Weakly compact cardinal Successor of Regular Cardinal Singular cofinality Jonsson cardinal super-Souslin tree Almost-disjoint family Uniformly coherent Open Access Erdos-Hajnal graphs Slim tree stationary reflection Strongly compact cardinal Fast club Partition relations for trees Rado's conjecture free Boolean algebra Dushnik-Miller Knaster and friends Sierpinski's onto mapping principle Almost countably chromatic Martin's Axiom Foundations Subtle tree property Prevalent singular cardinals OCA Monotonically far Hindman's Theorem Intersection model Partition Relations Axiom R weak diamond Was Ulam right? Countryman line tensor product graph Well-behaved magma Uniformly homogeneous Almost Souslin Square-Brackets Partition Relations GMA Interval topology on trees Generalized descriptive set theory P-Ideal Dichotomy Parameterized proxy principle Analytic sets Cardinal function diamond star Diamond-sharp Souslin Tree Closed coloring unbounded function Iterated forcing 54G20 Local Club Condensation. Reflecting stationary set HOD weak square Filter reflection b-scale coloring number Ostaszewski square Forcing with side conditions Fat stationary set ZFC construction Ascent Path AIM forcing Club Guessing Constructible Universe Minimal Walks Fodor-type reflection Prikry-type forcing Ulam matrix club_AD Amenable C-sequence Cohen real Dowker space xbox stick Forcing Commutative projection system reflection principles Nonspecial tree polarized partition relation projective Boolean algebra strongly bounded groups Luzin set free Souslin tree Generalized Clubs stationary hitting PFA incompactness Non-saturation higher Baire space Ascending path nonmeager set indecomposable filter Vanishing levels Large Cardinals Microscopic Approach positive partition relation Shelah's Strong Hypothesis specializable Souslin tree Strong coloring S-Space Subnormal ideal Hereditarily Lindelöf space Postprocessing function O-space full tree Diamond Respecting tree Entangled linear order Poset Kurepa Hypothesis Subadditive Sakurai's Bell inequality square Knaster Chang's conjecture Sigma-Prikry Whitehead Problem Greatly Mahlo Diamond for trees Antichain Chromatic number middle diamond transformations Small forcing
Blog Archives
40th summer conference on topology and its applications
I gave an invited talk at the General and Set-Theoretic Topology session of the 40th summer conference on topology and its applications, July 2026. Talk title: A tree-based perfectly normal space whose square is not countably metacompact. Abstract. The study … Continue reading
Posted in Invited Talks, Topology
Tagged Interval topology on trees
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Proxy principles in combinatorial set theory
Joint work with Ari Meir Brodsky and Shira Yadai. Abstract. The parameterized proxy principles were introduced by Brodsky and Rinot in a 2017 paper as new foundations for the construction of $\kappa$-Souslin trees in a uniform way that does not … 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
Distributive Aronszajn trees
Joint work with Ari Meir Brodsky. Abstract. Ben-David and Shelah proved that if $\lambda$ is a singular strong-limit cardinal and $2^\lambda=\lambda^+$, then $\square^*_\lambda$ entails the existence of a $\lambda$-distributive $\lambda^+$-Aronszajn tree. Here, it is proved that the same conclusion remains … Continue reading
More notions of forcing add a Souslin tree
Joint work with Ari Meir Brodsky. Abstract. An $\aleph_1$-Souslin tree is a complicated combinatorial object whose existence cannot be decided on the grounds of ZFC alone. But 15 years after Tennenbaum and independently Jech devised notions of forcing for introducing … 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
