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Uniformization Martin's Axiom reflection principles Square-Brackets Partition Relations specializable Souslin tree coloring number Well-behaved magma Dowker space Foundations xbox Fast club Successor of Regular Cardinal Club Guessing Closed coloring Large Cardinals Forcing GMA Rado's conjecture diamond star Axiom R free Boolean algebra Hereditarily Lindelöf space O-space Knaster Strongly compact cardinal transformations 54G20 square principles approachability ideal Diamond for trees Successor of Singular Cardinal free Souslin tree Universal Sequences Diamond-sharp nonmeager set Subtle tree property ccc Sakurai's Bell inequality HOD incompactness Rock n' Roll S-Space Ostaszewski square Precaliber Erdos-Hajnal graphs Partition Relations Constructible Universe Small forcing SNR Nonspecial tree Uniformly homogeneous Distributive tree club_AD Intersection model Amenable C-sequence Lipschitz reduction Subadditive PFA Diamond Knaster and friends Absoluteness Non-saturation Was Ulam right Analytic sets ZFC construction Weakly compact cardinal higher Baire space countably metacompact Singular cofinality Fat stationary set Uniformly coherent Shelah's Strong Hypothesis Hindman's Theorem Mandelbrot set Ulam matrix sap AIM forcing very good scale strongly bounded groups Local Club Condensation. weak diamond Commutative projection system Hedetniemi's conjecture Almost Souslin Strongly Luzin set polarized partition relation Erdos Cardinal Prevalent singular cardinals Reflecting stationary set Ascent Path Subnormal ideal Jonsson cardinal Dushnik-Miller Vanishing levels Postprocessing function Aronszajn tree projective Boolean algebra Singular cardinals combinatorics Luzin set stick Prikry-type forcing Chromatic number Whitehead Problem Kurepa Hypothesis middle diamond Chang's conjecture Cardinal Invariants unbounded function b-scale Countryman line PFA(S)[S] C-sequence Respecting tree stationary hitting Strong coloring weak Kurepa tree Souslin Tree Generalized Clubs full tree super-Souslin tree Greatly Mahlo Subtle cardinal P-Ideal Dichotomy indecomposable ultrafilter Forcing Axioms Fodor-type reflection Poset Slim tree weak square OCA Cohen real L-space Minimal Walks square stationary reflection Coherent tree Almost countably chromatic Parameterized proxy principle positive partition relation Cardinal function Filter reflection Ramsey theory over partitions Antichain Rainbow sets Sigma-Prikry Ineffable cardinal Sierpinski's onto mapping principle Reduced Power Iterated forcing Almost-disjoint family Generalized descriptive set theory Selective Ultrafilter regressive Souslin tree Microscopic Approach Singular Density Open Access tensor product graph Commutative cancellative semigroups
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 $Vspec(\kappa)$ of sets that can be realized as the vanishing levels $V(\mathbf T)$ of a normal $\kappa$-tree $\mathbf T$. The latter is an invariant in … Continue reading
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
