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Sakurai's Bell inequality stationary hitting Prevalent singular cardinals Universal Sequences Strong coloring Fast club Successor of Regular Cardinal diamond star Ascending path Chang's conjecture nonmeager set unbounded function free Boolean algebra Successor of Singular Cardinal Hedetniemi's conjecture stationary reflection O-space Monotonically far weak diamond Well-behaved magma Ramsey theory over partitions Small forcing Postprocessing function Souslin Tree Interval topology on trees specializable Souslin tree 54G20 Generalized descriptive set theory Diamond for trees Cardinal function Dushnik-Miller middle diamond very good scale Aronszajn tree Selective Ultrafilter Local Club Condensation. sap Shelah's Strong Hypothesis Subadditive Erdos-Hajnal graphs OCA Uniformly homogeneous Ulam matrix Was Ulam right? Intersection model Luzin set Non-saturation perfectly normal Parameterized proxy principle xbox countably metacompact Open Access projective Boolean algebra Square-Brackets Partition Relations Dowker space Fodor-type reflection ccc Entangled linear order strongly bounded groups b-scale square principles Vanishing levels Rock n' Roll Uniformly coherent higher Baire space Subnormal ideal Ostaszewski square Commutative projection system Countryman line Nonspecial tree Axiom R indecomposable filter Almost countably chromatic Reflecting stationary set Uniformization Singular cardinals combinatorics Slim tree PFA Prikry-type forcing coloring number Iterated forcing stick Strongly compact cardinal approachability ideal PFA(S)[S] Fat stationary set transformations Constructible Universe incompactness C-sequence reflection principles weak Kurepa tree Chromatic number square Poset Lipschitz reduction Coherent tree Forcing Axioms AIM forcing Martin's Axiom Sierpinski's onto mapping principle Almost Souslin Ascent Path HOD free Souslin tree S-Space GMA Antichain club_AD Club Guessing Knaster Knaster and friends Respecting tree Singular Density Rainbow sets ZFC construction Diamond Ineffable cardinal Analytic sets Foundations Forcing with side conditions Forcing Mandelbrot set Jonsson cardinal polarized partition relation Large Cardinals weak square P-Ideal Dichotomy Kurepa Hypothesis Minimal Walks Diamond-sharp Reduced Power L-space Cardinal Invariants Erdos Cardinal positive partition relation Weakly compact cardinal Commutative cancellative semigroups Absoluteness Strongly Luzin set Hindman's Theorem Partition Relations Rado's conjecture Precaliber Partition relations for trees Amenable C-sequence Microscopic Approach Sigma-Prikry Hereditarily Lindelöf space Filter reflection Distributive tree Subtle cardinal SNR Closed coloring full tree Subtle tree property super-Souslin tree Almost-disjoint family regressive Souslin tree Cohen real Greatly Mahlo Generalized Clubs Whitehead Problem Singular cofinality tensor product graph
Tag Archives: Almost countably chromatic
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
Set Theory Programme on Large Cardinals and Forcing, September 2013
I gave an invited talk at the Large Cardinals and Forcing meeting, Erwin Schrödinger International Institute for Mathematical Physics, Vienna, September 23–27, 2013. Talk Title: Hedetniemi’s conjecture for uncountable graphs Abstract: It is proved that in Godel’s constructible universe, for … Continue reading
Posted in Invited Talks
Tagged Almost countably chromatic, Chromatic number, Hedetniemi's conjecture
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Chromatic numbers of graphs – large gaps
Abstract. We say that a graph $G$ is $(\aleph_0,\kappa)$-chromatic if $\text{Chr}(G)=\kappa$, while $\text{Chr}(G’)\le\aleph_0$ for any subgraph $G’$ of $G$ of size $<|G|$. The main result of this paper reads as follows. If $\square_\lambda+\text{CH}_\lambda$ holds for a given uncountable cardinal $\lambda$, … Continue reading
Posted in Compactness, Infinite Graphs, Publications
Tagged 03E35, 05C15, 05C63, Almost countably chromatic, Chromatic number, incompactness, Ostaszewski square
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