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