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Kurepa Hypothesis Subnormal ideal Rainbow sets Knaster and friends Generalized descriptive set theory SNR Ramsey theory over partitions Hereditarily Lindelöf space unbounded function PFA Cardinal Invariants Minimal Walks Absoluteness Sakurai's Bell inequality approachability ideal Entangled linear order Filter reflection Small forcing Coherent tree Countryman line Erdos Cardinal 54G20 Knaster Cardinal function Iterated forcing Martin's Axiom Strongly Luzin set Parameterized proxy principle Singular cofinality Diamond Jonsson cardinal weak square Uniformly homogeneous Cohen real countably metacompact ZFC construction Hedetniemi's conjecture transformations Prevalent singular cardinals stick O-space Singular cardinals combinatorics Fat stationary set PFA(S)[S] Monotonically far Strong coloring Well-behaved magma sap xbox Ascent Path super-Souslin tree Forcing with side conditions Closed coloring weak Kurepa tree Foundations Nonspecial tree Subtle cardinal Erdos-Hajnal graphs Generalized Clubs diamond star Lipschitz reduction Ostaszewski square strongly bounded groups polarized partition relation Partition Relations GMA Poset Interval topology on trees Almost Souslin Subtle tree property Reflecting stationary set Almost countably chromatic Luzin set Mandelbrot set Square-Brackets Partition Relations OCA Commutative projection system Selective Ultrafilter higher Baire space Intersection model Subadditive Ineffable cardinal indecomposable filter Slim tree Souslin Tree Hindman's Theorem L-space Diamond for trees Distributive tree Rock n' Roll Sigma-Prikry Almost-disjoint family club_AD P-Ideal Dichotomy Weakly compact cardinal tensor product graph Chromatic number Shelah's Strong Hypothesis middle diamond Successor of Singular Cardinal Analytic sets free Boolean algebra Diamond-sharp Forcing Fodor-type reflection very good scale positive partition relation Amenable C-sequence Vanishing levels Local Club Condensation. Whitehead Problem HOD Successor of Regular Cardinal Reduced Power Forcing Axioms Sierpinski's onto mapping principle Commutative cancellative semigroups Was Ulam right? Constructible Universe Postprocessing function perfectly normal Dowker space free Souslin tree stationary reflection Singular Density Chang's conjecture specializable Souslin tree Ascending path Prikry-type forcing projective Boolean algebra Club Guessing Dushnik-Miller full tree Precaliber ccc Strongly compact cardinal S-Space incompactness nonmeager set Large Cardinals Non-saturation Uniformization weak diamond Universal Sequences AIM forcing Rado's conjecture Greatly Mahlo Axiom R Aronszajn tree square principles stationary hitting Open Access C-sequence Antichain Uniformly coherent coloring number square b-scale Fast club Microscopic Approach Respecting tree reflection principles Ulam matrix regressive Souslin tree
Tag Archives: 05C63
Reflection on the coloring and chromatic numbers
Joint work with Chris Lambie-Hanson. Abstract. We prove that reflection of the coloring number of graphs is consistent with non-reflection of the chromatic number. Moreover, it is proved that incompactness for the chromatic number of graphs (with arbitrarily large gaps) … Continue reading
Posted in Compactness, Infinite Graphs, Publications
Tagged 03E35, 05C15, 05C63, Chang's conjecture, Chromatic number, coloring number, Fodor-type reflection, incompactness, Iterated forcing, Parameterized proxy principle, Postprocessing function, Rado's conjecture, square, stationary reflection
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Same Graph, Different Universe
Abstract. May the same graph admit two different chromatic numbers in two different universes? how about infinitely many different values? and can this be achieved without changing the cardinals structure? In this paper, it is proved that in Godel’s constructible … Continue reading
Posted in Infinite Graphs, Publications
Tagged 03E35, 05C15, 05C63, approachability ideal, Chromatic number, Constructible Universe, Forcing, Ostaszewski square
10 Comments
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
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
