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