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