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