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