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