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Non-saturation Uniformization C-sequence Sakurai's Bell inequality ccc Knaster and friends Intersection model strongly bounded groups Amenable C-sequence Cohen real Interval topology on trees Erdos-Hajnal graphs Sierpinski's onto mapping principle OCA Lipschitz reduction Strongly Luzin set PFA Absoluteness Strong coloring higher Baire space SNR Reduced Power Rock n' Roll Club Guessing Almost countably chromatic Jonsson cardinal Ulam matrix Fodor-type reflection Chang's conjecture approachability ideal Rainbow sets Coherent tree Diamond Axiom R Whitehead Problem Weakly compact cardinal square club_AD Ineffable cardinal middle diamond very good scale Hindman's Theorem 54G20 diamond star Commutative cancellative semigroups Slim tree weak diamond Uniformly coherent tensor product graph Open Access stationary hitting Entangled linear order Luzin set Minimal Walks Forcing Almost Souslin Selective Ultrafilter Almost-disjoint family Subadditive Distributive tree Successor of Regular Cardinal Kurepa Hypothesis Dushnik-Miller Hereditarily Lindelöf space Microscopic Approach Singular cofinality Filter reflection Vanishing levels Small forcing PFA(S)[S] Poset Generalized descriptive set theory Constructible Universe P-Ideal Dichotomy Foundations Postprocessing function Subtle tree property Ramsey theory over partitions Well-behaved magma Analytic sets Uniformly homogeneous perfectly normal Forcing with side conditions Cardinal Invariants HOD L-space Partition Relations Cardinal function projective Boolean algebra Subtle cardinal Strongly compact cardinal Diamond-sharp unbounded function Sigma-Prikry transformations b-scale Mandelbrot set Prikry-type forcing Erdos Cardinal Dowker space Closed coloring Local Club Condensation. Countryman line Ascent Path Greatly Mahlo full tree Souslin Tree Hedetniemi's conjecture Precaliber AIM forcing GMA incompactness stationary reflection Rado's conjecture coloring number xbox Monotonically far Iterated forcing indecomposable filter Antichain Chromatic number Prevalent singular cardinals Parameterized proxy principle Aronszajn tree Fat stationary set Singular Density Diamond for trees Respecting tree free Boolean algebra Shelah's Strong Hypothesis reflection principles Ostaszewski square O-space Generalized Clubs Universal Sequences square principles Martin's Axiom Commutative projection system Singular cardinals combinatorics Large Cardinals regressive Souslin tree stick Knaster Reflecting stationary set sap countably metacompact Fast club S-Space Partition relations for trees ZFC construction specializable Souslin tree super-Souslin tree free Souslin tree polarized partition relation Was Ulam right? Subnormal ideal weak square Square-Brackets Partition Relations weak Kurepa tree Ascending path Forcing Axioms positive partition relation nonmeager set Nonspecial tree Successor of Singular Cardinal
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
Comments Off on 40th summer conference on topology and its applications
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
The vanishing levels of a tree
Joint work with Shira Yadai and Zhixing You. Abstract. We initiate the study of the spectrum of sets that can be realized as the vanishing levels $V(\mathbf T)$ of a normal $\kappa$-tree $\mathbf T$. This is an invariant in the … Continue reading
Posted in Preprints, Souslin Hypothesis
Tagged Almost-disjoint family, Ascent Path, C-sequence, Coherent tree, Dowker space, Open Access, Parameterized proxy principle, regressive Souslin tree, Respecting tree, Subtle tree property, Uniformly homogeneous, Vanishing levels, weak Kurepa tree
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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
