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