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Subtle tree property Universal Sequences square Souslin Tree Prikry-type forcing Uniformization sap Diamond free Souslin tree Subadditive xbox Ramsey theory over partitions Martin's Axiom stationary hitting Rado's conjecture Reduced Power Strongly Luzin set P-Ideal Dichotomy positive partition relation OCA club_AD Dowker space Nonspecial tree weak Kurepa tree Successor of Regular Cardinal Reflecting stationary set weak diamond polarized partition relation Partition Relations Generalized descriptive set theory Kurepa Hypothesis Small forcing Selective Ultrafilter Ulam matrix Minimal Walks Was Ulam right? nonmeager set strongly bounded groups Whitehead Problem Uniformly coherent diamond star Hedetniemi's conjecture Large Cardinals Luzin set Ascent Path Sakurai's Bell inequality Absoluteness Non-saturation Slim tree Ineffable cardinal Uniformly homogeneous Foundations PFA Countryman line countably metacompact stick Subtle cardinal unbounded function Entangled linear order Constructible Universe Open Access full tree C-sequence Commutative projection system Forcing Axioms Iterated forcing reflection principles Sigma-Prikry square principles Strongly compact cardinal Hereditarily Lindelöf space Respecting tree Monotonically far b-scale Vanishing levels Fat stationary set Greatly Mahlo Parameterized proxy principle Erdos Cardinal Square-Brackets Partition Relations incompactness coloring number PFA(S)[S] middle diamond Intersection model Closed coloring Dushnik-Miller Local Club Condensation. Lipschitz reduction Well-behaved magma Diamond-sharp Singular Density super-Souslin tree Singular cofinality Cohen real Filter reflection tensor product graph Sierpinski's onto mapping principle Club Guessing projective Boolean algebra indecomposable filter Ostaszewski square Distributive tree stationary reflection Analytic sets Shelah's Strong Hypothesis Antichain Ascending path Generalized Clubs Chromatic number Almost Souslin Successor of Singular Cardinal Erdos-Hajnal graphs Forcing transformations Commutative cancellative semigroups Rock n' Roll AIM forcing Subnormal ideal Fodor-type reflection Mandelbrot set regressive Souslin tree Diamond for trees specializable Souslin tree Chang's conjecture Forcing with side conditions Strong coloring free Boolean algebra higher Baire space Axiom R perfectly normal approachability ideal very good scale Cardinal function Poset Aronszajn tree Coherent tree O-space S-Space Interval topology on trees ccc Rainbow sets Knaster and friends Cardinal Invariants Hindman's Theorem Postprocessing function Amenable C-sequence Knaster Precaliber SNR Almost countably chromatic weak square Microscopic Approach ZFC construction Almost-disjoint family GMA Weakly compact cardinal Jonsson cardinal Fast club Singular cardinals combinatorics HOD L-space Prevalent singular cardinals 54G20
Tag Archives: Respecting tree
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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Square with built-in diamond-plus
Joint work with Ralf Schindler. Abstract. We formulate combinatorial principles that combine the square principle with various strong forms of diamond, and prove that the strongest amongst them holds in $L$ for every infinite cardinal. As an application, we prove that … Continue reading
Posted in Publications, Squares and Diamonds
Tagged 03E05, 03E45, Almost Souslin, diamond star, Kurepa Hypothesis, Minimal Walks, Respecting 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
