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Uniformly coherent weak Kurepa tree L-space C-sequence Successor of Regular Cardinal Generalized Clubs Rock n' Roll O-space polarized partition relation Partition Relations Shelah's Strong Hypothesis Reflecting stationary set PFA(S)[S] Lipschitz reduction square PFA Rainbow sets Foundations ccc Whitehead Problem Uniformly homogeneous higher Baire space HOD strongly bounded groups Ulam matrix Fast club Greatly Mahlo Dushnik-Miller Jonsson cardinal Hedetniemi's conjecture Ostaszewski square transformations Amenable C-sequence Closed coloring Analytic sets Absoluteness Singular Density GMA Hereditarily Lindelöf space Diamond-sharp very good scale full tree Poset Martin's Axiom Sierpinski's onto mapping principle Fat stationary set Sakurai's Bell inequality Almost Souslin Non-saturation nonmeager set club_AD Almost-disjoint family Fodor-type reflection Luzin set Erdos Cardinal xbox projective Boolean algebra Filter reflection Reduced Power free Souslin tree SNR Square-Brackets Partition Relations Local Club Condensation. weak square Selective Ultrafilter Postprocessing function Rado's conjecture Prevalent singular cardinals Minimal Walks Sigma-Prikry Open Access diamond star Cohen real Large Cardinals Precaliber square principles tensor product graph Vanishing levels Ascent Path Cardinal function Strongly Luzin set middle diamond indecomposable ultrafilter Universal Sequences Slim tree Weakly compact cardinal Subtle cardinal Parameterized proxy principle Commutative cancellative semigroups Forcing Ramsey theory over partitions Singular cardinals combinatorics Knaster Knaster and friends free Boolean algebra Prikry-type forcing Generalized descriptive set theory Singular cofinality sap Subadditive b-scale Aronszajn tree specializable Souslin tree incompactness Forcing Axioms AIM forcing Souslin Tree Well-behaved magma Diamond Cardinal Invariants Axiom R stationary reflection Coherent tree Distributive tree Was Ulam right 54G20 weak diamond countably metacompact Club Guessing P-Ideal Dichotomy approachability ideal Small forcing Erdos-Hajnal graphs Nonspecial tree Uniformization stationary hitting reflection principles stick Strong coloring unbounded function Subtle tree property Dowker space Successor of Singular Cardinal S-Space Chang's conjecture OCA Mandelbrot set Microscopic Approach Chromatic number Antichain ZFC construction Almost countably chromatic regressive Souslin tree Diamond for trees Subnormal ideal positive partition relation Iterated forcing coloring number Constructible Universe Kurepa Hypothesis super-Souslin tree Ineffable cardinal Hindman's Theorem
Tag Archives: tensor product graph
Full Souslin trees at small cardinals
Joint work with Shira Yadai and Zhixing You. Abstract. A $\kappa$-tree is full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full $\kappa$-Souslin tree may consistently exist. Shelah gave an affirmative … Continue reading
Posted in Preprints, Souslin Hypothesis
Tagged Diamond for trees, full tree, Greatly Mahlo, Microscopic Approach, Parameterized proxy principle, Subtle cardinal, tensor product graph
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Hedetniemi’s conjecture for uncountable graphs
Abstract. It is proved that in Godel’s constructible universe, for every successor cardinal $\kappa$, there exist graphs $\mathcal G$ and $\mathcal H$ of size and chromatic number $\kappa$, for which the tensor product graph $\mathcal G\times\mathcal H$ is countably chromatic. … Continue reading