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