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