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